IAS 2016 — Maths

30g of sugar was mixed in 180 ml water in a vessel A, 40 g of sugar was mixed in 280 ml of water in vessel B and 20g of sugar was mixed in 100 ml of water in vessel C. The solution in vessel B is

A round archery target of diameter 1 m is marked with four scoring regions from the centre outwards as red, blue, yellow and white. The radius of the red band is 0.20 m. The width of all the remaining bands is equal. If archers throw arrows towards the target, what is the probability, that the arrows fall in the red region of the archery target?

The monthly average salary paid to all the employees of a company was Rs 5000. The monthly average salary paid to male and female employees was Rs 5200 and Rs 4200 respectively. Then the percentage of males employed in the company is:

Ram and Shyam work on a job together for four days and complete 60% of it. Ram takes leave then and Shyam works for eight more days to complete the job. How long would Ram take to complete the entire job alone?

In a class, there are 18 very tall boys. If these constitute three fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class?

A class starts at 11:00 am and lasts till 2:27 pm. Four periods of equal duration are held during this interval. After every period, a rest of 5 minutes is given to the students. The exact duration of each period is:

Anita's mathematics test had 70 problems carrying equal marks i.e., 10 arithmetic, 30 algebra and 30 geometry. Although she answered 70% of the arithmetic, 40% of the algebra and 60% of the geometry problems correctly, she did not pass the test because she got less than 60% marks. The number of more questions she would have to answer correctly to earn a 60% passing marks is:

A daily train is to be introduced between station A and station B starting from each at 6 AM and the journey is to be completed in 42 hours. What is the number of trains needed in order to maintain the Shuttle Service?

Two numbers X and Y are respectively 20% and 28% less than a third number Z. By what percentage is the number Y less than the number X?

There are five hobby clubs in a college —photography, yachting, chess, electronics and gardening. The gardening group meets every second day, the electronics group meets every third day, the chess group meets every fourth day, the yachting group meets every fifth day and the photography group meets every sixth day. How many times do all the five groups meet on the same day within 180 days?

A and B walk around a circular park. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other after 800 a.m. and before 9.30. a.m.?

W can do 25% of a work-in 30days, X can do 1/4 of the 110. work in 10 days, Y can do 40% of the work in 40 days and Z. can do 1/3 of the work in 13 days. Who will complete the work first?

A cylindrical overhead tank of radius 2m and height 7m is to be filled from an underground tank of size 5.5m × 4m × 6m. How much portion of the underground tank is still filled with water after filling the overhead tank completely?

There is an order of 19000 quantity of a particular product from a customer. The firm produces 1000 quantity of that product per day out of which 5% are unfit for sale. In how many days will the order be completed?

How many numbers are there between 100 and 300 which, either begin with or end with 2?

In a question paper there are five questions to be attempted and answer to each question has two choices—True (T) or False (F). It is given that no two candidates have given the answers to the five questions in an identical sequence. For this to happen the maximum number of candidates is:

The average monthly income of a person in a certain family 5 is ₹ 10,000. What will be the average monthly income of a person in the same family if the income of one person increased by ₹ 1,20,000 per year?

The total emoluments of two persons are the same, but one gets allowances to the extent of 65% of his basic pay and the other gets allowances to the extent of 80% of his basic pay. The ratio of the basic pay of the former to the basic pay of the latter is:

In a race, a competitor has to collect 6 apples which are kept a straight line on a track and a bucket is placed at the beginning of the track which is a starting point. The condition is that the competitor can pick only one apple at a time, run back with it and drop it in the bucket. If he has to drop all the apples in the bucket, how much total distance he has to run if the bucket is 5 meters from the first apple and all other apples are placed 3 meters apart?

A piece of tin is in the form of a rectangle having length 12cm and width 8 cm. This is used to construct a closed cube. The side of the cube is:

An agricultural field is in the form of a rectangle having length X1 meters and breadth X2 meters (X1 and X2 are variable). If X1 + X2 = 40 meters, then the area of the agricultural field will not exceed which one of the following values?

In aid of charity, every student in a class contributes as many rupees as the number of students in that class. With the additional contribution of 2 by one students only, the total collection is 443. Then how many students are there in the class?

AB is a vertical trunk of a huge tree with A being the point where the base of the trunk touches the ground. Due to a cyclone, the trunk has been broken at C which is at a height of 12 meters, broken part is partially attached to the vertical portion of the trunk at C. If the end of the broken part B touches the ground at D which is at a distance of 5 meters from A, then the original height of the trunk is:

If R and S are different integers both divisible by 5, then which of the following is not necessarily true?

The sum of the ages of 5 members comprising a family, 3 years ago, was 80 years. The average age of the family today is the same as it was 3 years ago, because of an addition of a baby during the intervening period. How old is the baby?

A person allows 10% discount for cash payment from the marked price of a toy and still he makes a 10% gain. What is the cost price of the toy which is marked Rs 770?

There are some nectar-filled flowers on a tree and some bees are hovering on it. If one bee lands on each flower, one bee will be left out. If two bees land on each flower, one flower will be left out. The number of flowers and bees respectively are: