CUET UG 2025 — Arithmetic

Consider the following frequency distribution. | Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | |---|---|---|---|---|---|---|---| | Frequency | 4 | 5 | 7 | 10 | 12 | 8 | 4 | Find the median of the distribution?

X, Y and Z together can do a piece of work in 16 (4/11) days. X and Y together can do the same work in 20 days. In how many days will Z alone finish the 60% of the work?

If the mean of five observations x + 1, x + 2, x + 3, x + 4 and x + 5 is 15, then what is the mean of the first three observations?

Amit is walking at a speed of 10 km/hr. After every kilometer, he takes a rest for 5 minutes. What is the time taken to cover a distance of 5 kilometers by Amit?

The difference between cost price (CP) and selling price (SP) of an article is Rs 240. If the profit is 20%, then the selling price is

Consider the simple interest of the following (A) The simple interest on Rs 8,930 at 6% per annum for 5 years (B) The simple interest on Rs 3,080 at 13.50% per annum for 4 years (C) The simple interest on Rs 7,200 at 14.00 % per annum for 7 years (D) The simple interest on Rs. 3,120 at 4.00 % per annum for 5 years The simple interests of these in increasing order are: Choose the correct answer from the options given below:

Two mobile phones were purchased at the same price. One was sold at a profit of 20% and the second was sold at a price which was Rs.1520 less than the price at which the first was sold. If the overall profit earned by selling both the mobile phones was 1%, then determine the cost price of one mobile?

A man's wage was reduced by 50%. Again, the reduced wage was increased by 50%. Find his loss in terms of percentage:

The ratio of the rate of flow of water through pipes varies inversely, as the square of the radius of the pipes. What is the ratio of the rates of flow in two pipes of diameter 2 cm and 4 cm?

P and Q can do work separately in 10 and 20 days, respectively. In how many days can they finish it, working together?

There are 48 students in a college gathering. The ratio of the number of boys to the number of girls in the gathering is 5:3. If the ratio of the boys to girls has to be made 6:5, then how many girls need to be added to the gathering, without changing the numbers of boys who are attending the gathering?

Consider the compound interest of the following (A) The compound interest on Rs 30500 at 15% per annum for 2 years, (compounded annually) is: Rs. 9836.25 (B) The compound interest of Rs 5000 at 20% per annum for one year is compounded (half-yearly) is: Rs. 6050. Which of the following statements is / are correct?

The owner of a garment shop labelled his articles at 25% above the cost-price. Due to a slump in the market, his cost price was reduced by 5% but he keeps the marked price same. He thus offers a discount of 8%, due to which the sales increase by 25%. Calculate the change in owner's profit?

In a school bus, there are 54 students, the ratio of boys to girls is 5:4. If 3 boys leave the bus at their stop, the ratio of boys to girls would be ?

The median of the observations: 12, 59, 14, 46, 18, 42, 26, 33, 22 is:

Mr. X invested one fourth of his capital at 8%, one third at 7% and the remaining part at 10%. If his annual simple interest on this investment is Rs 510, then the total capital invested by Mr. X is?

A shopkeeper buys $500$ m of electronic wire at $50$ paise per m. He sold $50$ % of the wire at a profit of $5$ %. At what percent should the shopkeeper sell the remaining wire so as to gain $10$% on the whole transaction?

'A' can build up a structure in 8 days and 'B' can break it in 3 days. 'A' worked building for 4 days and then 'B' joined and start breaking while 'A' kept building for another 2 days. In how many days will 'A' alone build up the remaining part of the structure?

The average of $39$ numbers is $17$. Each number is multiplied by $12$ and then $16$ is added to each number. Finally, each number thus formed is divided by $11$. $$\newline$$ Determine the average of the new sets of numbers thus formed ?

A car covers a certain distance in 7 hours with a uniform speed. The same distance could have been covered in 6 hours if the speed of the car was increased by 10 Km/h. What is the distance covered?

Two numbers a and b are in the ratio 3:2 and their sum is 25. The value of a is?

A, B and C can do some work in 40 days. A and C together can do twice as much work as B alone. Find the time taken by B to do the whole work.

If the cost-price of 18 articles is equal to the selling price of 15 articles, then find the gain percentage?

The mode and median of a set of 7 observations are 22.72 and 49.28, respectively. If each of the largest 3 observations of the set is increased by 4, then the median of the new set?

A sum of money becomes thrice of itself in 20 years. Find the simple interest rate per annum?

If P: Q: R = 2:3:4, then find: $\frac{P}{Q}:\frac{Q}{R}:\frac{R}{P}$

A and B, working separately can do a piece of work in 12 days and 20 days respectively. If they work alternately, beginning with A, then in how many days can the work be completed?

By selling 32 apples for Rs 30, a man loses 25%. How many apples should be sold for Rs 24, to gain 20% in the transaction?

A certain sum becomes 3-fold at 4% annual rate of interest. At what rate, will it become 6-fold?

Find out the median of the following frequency distribution: | Variable | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | Total | |---|---|---|---|---|---|---|---|---|---| | Frequency | 5 | 7 | 11 | 9 | 8 | 7 | 3 | 5 | 55 |

A boy is running at a speed of p km/hr to cover a distance of 1 km. But, due to the slippery ground, his speed is reduced by q km/hr (p>q). If he takes r hours to cover the distance, then

The simple interest on Rs 7200 at 14% per annum for 7 years is:

Read the information given in the table carefully and answer the question that follows: NUMBER OF CALCULATORS SOLD BY SHOPS P, Q, R, & S IN JUNE, JULY AND AUGUST | STATIONERY SHOP | JUNE | JULY | AUGUST | |-----------------|------|------|--------| | P | 112 | 100 | 130 | | Q | 100 | 88 | 124 | | R | 110 | 80 | 46 | | S | 96 | 94 | 86 | (A) The difference between the total number of calculators sold by shops P and Q together in August and the number of calculators sold by shops R and S together in June is 42 (B) The average number of calculators sold by Shop S in the three months is 92 (C) The respective ratio between the total number of calculators sold by shops P and Q in July and the total number of calculators sold by shop Q in August is 45 : 31 Choose the correct answer from the options given below:

(A) If a product's price is decreased by 25 % and then increased by 20 %, then the net change in the price of the product, is : decrease by 10% (B) If a product's price is increased by 15 % and then again increased by 20 %, then the net change in the price of the product, is : Increase by 38 % Choose the correct option(s):

A female deposit 10% of her salary in PF. She saves 30% of the remaining. The ratio of her expense on medicine and groceries is 3/4 of the remaining salary after saving. If her expenses on the medicine is Rs 2700, find the monthly salary.

Consider the following distribution. | Class Interval | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 | |---|---|---|---|---|---| | Frequency | 17 | 28 | 32 | f | 19 | f the mean of the above distribution is 50, find the value of f.

If in a class, 10 % of the girls are equal to one-fourth of the boys in the school, then the ratio of girls to the boys in the school is?

P and Q together can do a job in 6 days. Q and R can finish the same job in 60/7 days. P started the work and worked for 3 days. Q and R continued for 6 days and finish the work. Then, the difference of days in which R and P , independently can complete the job is:

Read the information given below carefully and answer the question that follows: (A) If the mean of 5 numbers is 15 and then if 27 is included to the numbers, then the mean of the 6 numbers shall be 17 (B) The mean of marks of 300 students is 60, the mean of the top 100 students' marks is 80 and the mean of the last 100 students is 50, then the mean of the marks of the rest of the 100 students of the group is 60. (C) The mean and median of 5 observations is 9 and 8 respectively, if 1 is subtracted from each observation, then the new mean and median shall be 8 and 7 respectively Choose the correct answer from the options given below:

If m is proportional to n and m = 5 when n =4, then what is the value of m when n = 18?

In an examination, out of 480 students, 85 % of girls and 70 % of boys pass. How many boys appeared for the examination, if the total pass percentage of the examination is 75 %?

Two cyclists, k kilometers apart, and starting at the same time, would be together in r hours if they traveled in the same directions, but would pass each other in t hours if they travelled in opposite directions. The ratio of the speed of the faster cyclist to that of the slower is:

A and B can complete a job in 24 days working together. A alone can complete it in 32 days. Both of them worked together for 8 days and then A left. The number of days B will take to complete the remaining job is:

The simple interest on a certain sum of money at 5% per annum for 4 years and 3 years differs by Rs. 42. What is the sum?

Ananyaa travels a certain distance at a speed of 3 kmph and reaches her destination late by 15 minutes. If she travels at a speed of 4 kmph, she reaches her destination 15 minutes earlier. Find the distance that Ananyaa is traveling to reach her destination.

If a saree is sold for Rs. 2880, the seller will incur a loss of 10%. At what price should he sell it to gain a profit of 20%?

One-half of a certain number is equal to 65% of the second number. What is the ratio of the first number to second number?

The ratio of speeds of a train and a car is 16:15, respectively. A bus covers a distance of 480 km in 8 hours. If the speed of the bus is 3/4th of the speed of the train, then the distance covered by the car in 6 hours is:

What is the compound interest earned on Rs. 80,000 at 40% per annum in one year, compounded quarterly?

18 women complete a work in 24 days and 24 men complete the same work in 15 days. 16 women worked for 3 days and then they left. 20 men worked for the next 2 days, and then they are joined by 16 women. In how many days will they finish the remaining work?

If the difference between 62% and 80% of a number is 198, then the difference between 92% and 56% of the number will be:

If the data is not following a symmetrical distribution, then the relationship between mean, median and mode is:

Two numbers are in the ratio 3:5. If 3 is subtracted from the first number and 3 is added to the second number, the ratio becomes 1:3. The sum of the numbers is?

Piyush covers a certain distance on bike. Had he moved 3 km/h faster, he would have taken 20 min less. If he had moved 2 km/h slower, he would have taken 20 min more. The distance covered (in km) is:

A sum of money becomes ₹ 20070 after 3 year and ₹ 30105 after 6 years on compound interest. The sum will be

6 goats or 8 sheeps can graze a field in 50 days. 8 goats and 6 sheeps can graze the field in:

In a moderately asymmetrical distribution, the mode and mean are 31.5 and 34.5, respectively. Calculate the median:

The price of an article, passing through three hands, rises on the whole by 61%, if the first and the second sellers earned 15% and 20% profit respectively, find the percentage profit earned by the third seller.

If $\sqrt{2}:(1 + \sqrt{3}) :: \sqrt{6}: x$, then $x$ is equal to:

By selling 8 pens for Rs 75, a shopkeeper loses 25%. How many pens should be sold for Rs 372 to earn a 24% profit?

A sales agent travels a distance of 50 km in 2 hours and 30 minutes. How much faster, in kilometres per hour, on average, must he travel to make such a trip in 5/6 hours less time?

Consider the compound interest of the following (A) The compound interest on Rs 16000 at 20% per annum for 9 months, compounded quarterly is: Rs 2522 (B) The compound interest on Rs 2800 at 10% per annum for 18 months, compounded annually is: Rs 434 Choose the correct statement(s):

A and B can do a piece of work in 12 days; B and C together can do it in 15 days. If A is twice as good a workman as C, find the number of days in which B alone can do the work?

Two dogs are standing 960 m apart from each other. The first dog runs at a speed of 9 m/s and the second runs at a speed of 7 m/s. If two dogs run towards each other, after how much time will they bump into each other?

The simple interest on a sum of Rs 1550 for 2 yrs is Rs 20 more than the simple interest on Rs 1450 for the same duration (the rate of interest is the same in both the cases). Find the rate of interest.

A person rows a boat 10 kms along the stream in 30 minutes and returns to the starting point in 40 minutes. The speed of the stream is:

A and B working together can finish a piece of work in 12 days while B alone can finish the same work in 30 days. Then determine that in how many days can A alone finish the same work?

Find the median of the following observations. 6, 49, 14, 46, 16, 42, 26, 32, 28

If 36: 84 :: 42: X, then the value of X, is:

P and Q together can do a piece of work in 60 days. Q and R together can do it in 120 days. P and R together can do it in 90 days. In what time can Q alone do the same work?

Ram, Shyam and Hari can complete a work in 20, 25 and 30 days, respectively. Consider the following statements: (A) Ram and Shyam together will complete the work in $11\frac{1}{9}$ days. (B) Shyam and Hari together will complete the work in 14 days. Choose the correct answer from the options given below:

A bus passes two persons moving in the direction of the moving bus at a speed of 3 km/hr and 5 km/hr, respectively. The bus passes the first person in 10 s and the second person in 11 s. Find the speed of the bus.

The age distribution of 40 children is as follows | Age (in yr.) | 5 - 6 | 6 - 7 | 7 - 8 | 8 - 9 | 9 - 10 | 10 - 11 | |---|---|---|---|---|---|---| | No. of children | 4 | 7 | 9 | 12 | 6 | 2 | Consider the following statements in respect of the above frequency distribution. (A) The median of the age distribution is 7 yr. (B) 70% of the children are in the age group 6-9 yr. (C) The modal class of the children is 8-9 yr. Which of the above statements are true? Choose the correct answer from the options given below:

Consider the compound interest in the following cases: (A) The compound interest on Rs 16000 at 20% per annum for 9 months, compounded quarterly is Rs. 2500 (B) The compound interest on Rs 2800 at 10% per annum for 18 months is Rs. 434. Choose the correct statement(s):

The monthly salary of A, B and C are in the ratio 2:3: 5. If C's monthly salary is Rs.1200 more than that of A, then B's annual salary is:

Profit earned by selling an article for Rs.1060 is 20% more than the loss incurred by selling the article for Rs.950. At what price should the article be sold to earn a 20% profit?

If $\frac{1}{a} : \frac{1}{b} : \frac{1}{c} = 3 : 4 : 2$, then determine a:b:c.

In what time will the simple interest on ₹2200 at 6% per annum be the same as that on ₹1650 at 9% per annum in 10 years?

X sold an article to Y at a profit of 18%. Later on, Y sold it back to X at a profit of 40%, thereby gaining ₹ 118. How much did X pay for the article originally?

The mean of 6 numbers is 19. If two more numbers are included, the mean of the 8 numbers becomes 23. What is the sum of the two included numbers?

8 men and 3 boys together can complete a piece of work in 5 days. If 5 boys can complete the same piece of work in 15 days, in how many days do 5 men complete the same piece of work?

In how many years will a sum of money double itself at 12.5% p.a., at simple interest?

A boat covers 150 km downstream and 40 km upstream in 4 hours while it covers 70 km downstream and 24 km upstream in 2 hours. Determine the velocity of the current?

If $a:b = \frac{12}{5}:\frac{3}{10}$ and $b:c = \frac{7}{9}:\frac{12}{7}$ then $a:c$ is

Match List-I with List-II | List-I | List-II | |---|---| | (A) 37.5% of 64 | (I) 7 | | (B) 14% of 50 | (II) 54 | | (C) 65% of 80 | (III) 24 | | (D) 75% of 72 | (IV) 52 | Choose the correct answer from the options given below:

The median of the given data is: 7, 5, 2, 3, 6, 9, 1

If a certain sum becomes three times in 4 years at compound interest, then in how many years, will it become 9 times?

A cyclist covers a distance of 170 meters in 17 seconds. The time taken by the cyclist to cover the distance of 6 km, shall be how much?

A can do a work in 4 days, B can do same work in 8 days, then the time taken by A and B to do the same work together is:

If selling price of an article is $\frac{7}{6}$ of its cost price. Then the profit percentage in the transaction is:

P can build a wall in the same time in which Q and R together can do it. If P and Q together could do it in 30 days and R alone in 40 days, in what time could Q alone do it?

A motor boat can travel at 15km/hr in still water. It traveled 63 km downstream in a river and then returned taking altogether 10 hr. What is the rate of flow of the river?

There exist three numbers in the ratio of 3 : 2 : 7 such that the sum of their squares is equal to 558. The three numbers will be respectively:

2, 4, 5, 2, 4, 8, 2, 4, 7, 8, 12, 4, The mode of given data is:

The average of marks of 15 papers is 45. The average of marks of the first 8 papers is 48 and that of the last 8 papers is 40. The marks of the eight paper will be:

Read the information given below carefully and answer the question that follows: (A) The mean of 20 observations is 17. On checking, it was found that two observations were wrongly copied as 3 and 6. If the wrong observations are replaced by correct values 8 and 9, then the correct mean will be 16.4. (B) The ratio of $4^{3.5} : 2^5$ is same as 4 : 1 (C) The ratio of 1.5 : 2.5 can also be written as 3 : 5 (D) If : 2A = 3B = 4C, then, A : B : C is equal to 6 : 4 : 3 Choose the correct option:

In an election contested by only two candidates, one candidate got 30% of the total votes cast and lost by 500 votes. Determine the total number of votes that were cast in the elections?

A man traveled from the village to the post-office at the rate of 25 km/hr and walked back at the rate of 4 km/hr. If the whole journey took 5 hours 48 minutes, find the distance of the post-office from the village.

Two numbers are in the ratio of 3:5. If 9 is subtracted from each, the ratio becomes 12:23. Find the greater number.

4 men and 6 women can complete a job in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women take to complete the same job?

P, Q, R and S have ₹120, ₹130, ₹140 and ₹150 respectively when they go to visit a fair. P spends ₹49, Q spends ₹54, R spends ₹55 and S spends ₹58. Who has done the lowest expenditure proportionate to their resources?

A sum of money becomes ₹5100 after 3 years and ₹5950 after 4 years on compound interest. The rate of interest per annum is:

Match List-I with List-II | List-I | List-II | |---|---| | (A) 17% of 1200 | (I) 198 | | (B) 18% of 1100 | (II) 204 | | (C) 19% of 1000 | (III) 200 | | (D) 40% of 500 | (IV) 190 | Choose the correct answer from the options given below:

If the difference between the compound and simple interests on a certain sum of money for 2 years at 20% per annum is ₹ 64, then the sum in ₹ will be:

A train passes a 200 m long platform in 40 seconds and a man standing on the platform in 25 seconds. The speed of the train (km/hr) is:

A can complete a work in 16 days, working 6 hours a day. B can complete the same work in 12 days, working 9 hours a day. If both A and B work together, working 8 hours a day, in how many days can they complete the work?

Three milkmen rented a pasture, sharing the rent based on their individual use. A grazed 11 cows for 5 months, B grazed 9 cows for 4 months and C grazed 15 cows for 6 months. If A's share of rent is ₹ 1210, then C's share (in ₹) will be:

The Mean and Median of 7 observations are 10 and 9, respectively. If 2 is subtracted from each observation, then the new Median and the new Mean will be:

The relation between Mean, Median and Mode for symmetrical distribution is:

A trader sells wheat at 10% profit and uses weight 10% less than the actual measure. What is his actual percentage gain?

3 men or 15 boys can do a piece of work in 30 days. In how many days will 2 men and 5 boys do this work?

A boy travels between point A and point B at a speed of 6 km/h and returns at a speed of 9 km/h. If the total time taken by him is 1 hour 15 min, the distance between A and B is:

If 10% of X = 15% of Y = 1/5 of Z, then X: Y: Z is

Ram can do a piece of work in 10 days and Anshu in 20 days. They work together but 2 days before the completion of the work, Ram leaves and Anshu completes the work. In total how many days was the work completed?

The average of nine numbers is 50. The average of the first five numbers is 54 and the average of the last three numbers is 52. Find the sixth number of this set of numbers?

The median of the observations 1, 13, 7, 19, 18, 15, 32, 28, 23, 24, 31 is:

A and B started together to cover a certain distance, at a speed of 8 km/h and 10 km/h, respectively. If A arrives 15 minutes after B, then find the distance.

The sum of three numbers, namely, A, B and C is 156. The numbers A and B are in the ratio of 2:5, while B and C are in the ratio of 1:9. Find number B?

A certain amount, when put at a compound rate of interest, becomes double in 5 years. In how many years will the amount become eight times?

Arrange the following in ascending order. (A) 12.5% of 1960 (B) 5% of 6000 (C) 9% of 3000 (D) 11% of 2000 Choose the correct answer from the options given below:

In the first 9 matches of a cricket tournament, the wickets taken by Jumpo are as follows: 3 2 0 1 3 0 5 1 4 Find the median of the number of wickets taken by Jumpo?

The marks out of 50 obtained by 100 students in a test are given below as: | Marks obtained | 20 | 25 | 28 | 29 | 33 | 38 | 42 | 43 | |---|---|---|---|---|---|---|---|---| | Number of students | 6 | 20 | 24 | 28 | 15 | 4 | 2 | 1 | Find the value of the (3 mode - 2 median).

Arrange the simple interest of the following cases in decreasing order- (A) The simple interest on Rs 6600 at 5% per annum for 2 yrs. (B) The simple interest on Rs 200 at 6% per annum for 5 yrs. (C) The simple interest on Rs 840 at 5% per annum for 4 yrs. (D) The simple interest on Rs 5000 at 12% per annum for 2 yrs. Choose the correct answer from the options given below:

P and Q can complete a job in 24 days working together. P can alone complete it in 32 days. Both of them worked together for 8 days and then P left. The number of days Q will take to complete the remaining job is:

Ram purchased a watch at a cost of $(\frac{9}{10})^{th}$ of the original cost and sold at 8% more than the original cost. His profit/loss is

During a journey of 200 Km, the average speed of a car is 125 km/h. But if for the first 100 km, the driver increases its earlier average speed by 20% and then decreases it to its (2/3)rd for next 100 km. What will be the new average speed?

P completed $\frac{2}{5}$ part of certain work in 12 days. Further, Q completed the rest of the work in 18 days. In how many days could P and Q complete the work, if they worked together?

What is the rate of simple interest for the last 5 years if the sum of ₹ 480 becomes ₹ 792 in 11 years and the rate of interest for the first 6 years is 5%?

Arrange the following in decreasing order. (A) 24% of 25 (B) 18% of 30 (C) 11% of 55 (D) 16% of 50 Choose the correct answer from the options given below:

The median and mean of 7 observations are 9 and 11 respectively. If 2 is subtracted from each observation, then the new median and the new mean will respectively be which of the following?

The median of a set of 11 distinct observations is 22.5. If each of the largest 5 observations of the set is increased by 5, then the median of the new set

Arrange the following cases in ascending order in terms of number of days to complete the same work. (A) P can do (1/3)rd of the work in 5 days. (B) Q can do (1/6)th of the work in 4 days. (C) R can do 25% of the work in 4 days. (D) S can do 35% of the work in 7 days. Choose the correct answer from the options given below:

P travels in his car and covers 2/5 part of his journey at a speed of 20 km/h, 1/8 part at 5 km/h and the remaining 19/40 part at 19 km/h. What is the average speed of the car during the entire journey?

By selling a T-shirt on marked price of ₹ 650, a shopkeeper gains 25%. During a clearance sale, the shopkeeper allows a discount of 20% on the marked price. What is the overall profit/loss?

If the interest is payable annually, then the principal amount on which the compound interest for 2 years at 5% per annum is ₹ 369, is given by

Rs 30000 is lent at compound interest of 7 % per annum for 2 years. Find out the amount after two years.

To complete a work, Aditi takes 60 % more time than Bimla. If both of them work together, they take 16 days to complete the work. How much time shall Bimla take to do it alone?

If $\sqrt{6} : x :: \sqrt{3} : (1 + \sqrt{2})$, then x is equal to

Match List I with List II | List I | List II | |---|---| | Statistical Measure | Definition | | (A) Mode | (I) Sum of all observations divided by their count | | (B) Median | (II) Measure of the spread from the mean | | (C) Mean | (III) Central value when observations are arranged in order | | (D) Standard Deviation | (IV) Observation which has the highest frequency | Choose the correct answer from the options given below:

Two trains of equal length are running from the same origin on parallel tracks in the same direction, at the speeds of 58 km/hr and 73 km/hr, respectively. The faster train passes the other train in 144 seconds. What is the length (in meters) of each train?

A person sold two watches for Rs 5500 each. In the sale of the first watch, he made a profit of 20% and in the sale of the second watch, he incurred a 20% loss. What is his gain or loss percentage in total?

30 boys are engaged to do a piece of work in 15 days but it is found that in 5 days, 3/5 work is completed. How many boys may be allowed to go off, so that the work may be finished on time?

The profit earned after selling an item for ₹ 797 is the same as the loss incurred after selling the same item for ₹ 635. What is the cost price of the item?

What is the present worth of ₹ 161 due in 3 years at 5% simple interest per annum?

A man bought 400 m of fabric @ Rs. 60 per metre. He sold 50% of it at a profit of 4%. At what percent should he sell the remaining to gain 12% on the whole transaction?

If $\frac{x}{y} = \frac{3}{5}$ and $\frac{y}{z} = \frac{5}{2}$ then $\frac{x^2 + z^2}{x^2 - z^2}$ would be

A Police officer sees a chain snatcher and runs to catch her from a distance of 50 metres. When the Police officer starts chasing the chain snatcher from a distance of 50 metres, the chain snatcher is running @ 2 metres per second. At the same time the Police Officer is chasing the chain snatcher @ 4 metres per second. Find the distance covered by the chain snatcher when the Police Officer shall be able to successfully catch her?

A sum of ₹ 5500 is lent out in two parts in such a way that the interest on one part at 12% for 4 years is equal to that on another part at 8% for 5 years. What will be the two parts of the sum?

In a class, the number of students who scored 61 or more marks is 30 and there are almost 39 students who have scored below 61 marks. If the average marks of the class is 48, then determine that what is the largest possible average marks of students who have scored below 61 marks?

Ajeeta and Sanjeeta undertake a project for ₹ 48000. Further, it is known that Ajeeta can finish the project in 24 days and Sanjeeta can finish the project in 40 days while working alone. If the project gets completed in just 10 days when Ranjeeta also helped them in completing the project, then determine the amount that Ranjeeta would have received, if they distributed the amount in proportion to their respective working capability?

Dittee has 10 purses and each of which having an average of 25 lipsticks in each purse. Further, it is known that each purse has a minimum of 8 lipsticks and none of the purse has identical number of lipsticks. Determine that what can be the maximum number of lipsticks that Dittee shall have in any of her purse?

A man can walk uphill at the rate of $2\frac{1}{2}$ $km/hr$ and down hill at the rate of $3\frac{1}{2}$ $km/hr$. If the total time required to walk a certain distance up the hill and return to the starting point is 4 hr. 36 min, then what is the distance walked up the hill by the man?

2 trains running in oppsite directions cross a stationary lady standing at a point named F in 26 seconds and 21 seconds respectively. Further, the 2 trains cross each other in 24 seconds. Determine the ratio of the speed of the 2 trains?