CUET UG 2025 — Arithmetic

A boat can row at the speed of 16 km/hr in still water. If the river is flowing at 8 km/hr, and it takes 8 hours for a round trip, then the distance between the two places is:

In 900 meters race, Ram gives Shyam a start of 150 meters and defeats him by 50 seconds. If the speed of Ram is 4.5 m/sec, then speed of Shyam is

The least positive integer x satisfying $29 \equiv x \pmod{5}$ is

A tank has two outlet pipes, A and B, which together take 6 hours to empty a full tank when they are opened simultaneously. The tank was initially half-full and both the outlets were opened, after an hour an inlet pipe was also opened. If the inlet alone can fill the empty tank in 4 hours, how much time will it now take to fill the tank completely?

Three varieties A, B and C of rice are mixed together in the ratio 1:1:3 respectively. The price of rice A is Rs 127 per kg and that of rice B is Rs 135 per kg. If the price of the mixture is Rs. 152 per kg, then the price per kg of rice of type C is:

Two pipes A and B can fill a tank in 20 minutes and 10 minutes respectively. Both pipes A and B are opened together for some time and then pipe B is turned off. If the tank is filled in 15 minutes, then find after how many minutes pipe B is turned off?

In a 500 m race, the ratio of speeds of two participants, A and B, is 4:5 respectively. If A has a start of 180 m, then the distance by which A wins is

The remainder when $(672 + 541 + 383 + 295 + 101 + 86)$ is divided by 3, is:

Pipe A can fill a tank in 24 hours and pipe B in 32 hours. If both the pipes are opened in an empty tank at the same time, then the time taken to fill the tank is:

The unit's digit in $13^{61}$ is

In what ratio must pulses at ₹72 per kg be mixed with pulses ₹90 per kg so that the mixture be worth ₹80 per kg?

Two runners A and B complete a 150 meters race in 24 seconds and 36 seconds respectively. By how many meters will A defeat B?

A man rows 24 km upstream in 6 hours and 36 km downstream in 6 hours each time, then the speed of the boat in the still water is

Siyaram has 100 kg apples, he sells a part of it at 8% profit and rest of it at 18% profit. The overall profit he earns is 14%. The quantity he sold at 18% profit is:

If it is 7:00 pm currently in the clock, what will the clock show (in am or pm) after 674 hours?

A boat covers a distance of 51 km downstream in 3 hours and takes $7\frac{2}{7}$ hours to cover the same distance upstream. If the boat's speed in still water is 12 km/hrs, then the speed of the stream is:

The unit's digit of $13^{13}$ is:

Two pipes P and Q can fill a tank in 26 minutes and 52 minutes respectively. Both the pipes are opened together for some time and then pipe P is closed. If the tank is filled in 26 minutes, then after how many minutes pipe P is closed?

The least non-negative remainder when $2^{75}$ is divided by 5 will be:-

Inlet Pipe A can fill a tank in 30 minutes, and outlet pipes B and C can empty the tank in 2 hours each. If all 3 pipes operate together, the tank will be filled in:

A boat covers a distance 24 km upstream and returns to the same point in a total of 4 hours. If the speed of boat in downstream is twice its speed in upstream, then the speed of boat in upstream is:

In a game, A can give 36 points to B, A can give 42 point to C, B can give 10 points to C. How many points make the game ?

From a container full of orange juice, 7.5 liters was drawn out and replaced by soda water. This process is repeated 5 more time. The ratio of quantity of orange juice and soda water left in the container is 4:5. How much liter of orange juice did the container originally had? [(Use:0.44) 1/6 = 0.802]

A runs 9 times slower than B. If B gives A a start of 80 meters, how far must be the wining post on the tracks so that A and B reach there at the same time?

A swimmer whose speed in swimming pool is 5 km/h, swims between two points in a river and returns back to starting point. He took 20 minutes more to cover the distance upstream than to cover downstream. If the speed of stream is 2 km/h, then the distance between two points is

The water and milk in two vessels are in the ratio:1:1 and 3:8 respectively. In what ratio, the mixtures in the vessels be mixed to obtain a new mixture containing water and milk in the ratio 4:7?

If $525 \equiv (10 + K)( {mod } 7)$ where $K \in \mathbb{N}$, then the least value of $K$ is:

Two pipes can fill a tank in 6 minutes and 12 minutes respectively, and a third pipe can empty the tank at the rate of 18 liters per minute. If all the pipes working together can fill the empty tank in 5 minutes, the capacity of the tank is:

Match List-I with List-II | List-I | List-II | |---|---| | (A) Unit's digit of $2^{11}$ | (I) 2 | | (B) Unit's digits of $11^{132}$ | (II) 1 | | (C) Remainder when $71 \times 73 \times 75$ is divided by 23 | (III) 4 | | (D) Remainder when $7^{30}$ is divided by 5 | (IV) 8 | Choose the correct answer from the options given below:

A man rows a boat such that it covers a distance upstream in twice the time taken by him to cover the same distance downstream. If the speed of stream is 5 km/h, the speed of boat in still water is:

In what ratio water must be added to dilute honey costing Rs.240 per litre so that resulting syrup would be Rs.180 per litre

Pipe A and B can fill a tank in 15 hours and 20 hours respectively. Pipe C can empty the tank in 25 hours. Pipes A, B and C works together but pipe C is closed after 10 hours , then time taken by pipe A and B to fill the remaining tank is:

In a 500 metres race, the ratio of speeds of two participants Meena and Kamal is 4:5 respectively. If Meena has a start of 200 metres, find the distance by which Meena wins.

It is currently 9:40 AM. What will be the time in next 610 hours?

Ravi's speed of rowing in still water is 6 km/hr. He rows between two points in a river and return to the same starting point. He took 30 minutes more to cover the distance upstream than downstream. If the speed of the stream is 3 km/hr, then the distance between the two points is:

Two pipes A and B can fill a tank in 5 hours and 6 hours respectively. Pipe C can empty it in 12 hours. If all three pipes are opened together, then the time taken to fill the tank is:

500 g of jaggery syrup has 30% jaggery in it. The quantity of jaggery that should be added to make it 50% of syrup is:

The speed of water current is half the speed of a motor boat. The motor boat travels 15 km downstream in 1 hour. Then the time taken to return to the starting point is:

Two pipes A and B can fill a tank respectively in 30 min and 45 min. Both A and B are opened together for some time and then pipe B is turned off. If the tank is filled in 20 min, then find after how many minutes the pipe B is turned off?

The digit in the unit's place of $6^{500}$ is:

In a 200 m race, Rohan completes the race in 8 seconds and Vivan completes the race in 10 seconds. By how much distance Rohan beats Vivan?

In what ratio must rice at ₹ 60 per kg is mixed with rice at ₹ 90 per kg so that the mixture be worth ₹ 80 per kg?

400 g of apple vinegar has 40% apple juice in it. The amount of apple juice, which should be added to make it 60% in apple vinegar, is:

In a kilometer race P runs at 10 m/sec, Q runs at 5 m/sec then which of the following statement(s) is/ are correct ? (A) P wins the race in 100 sec (B) Q wins the race in 100 sec (C) P defeats Q by 500 m (D) Q defeats P by 500 m Choose the correct answer from the options given below:

The unit's digit of $2^{2025}$ is

Three pipes A, B & C fill a tank in 3 hours working simultaneously. The pipe C is twice as faster as B and B is twice as fast as A. The time taken by pipe A alone to fill the tank is:

The ratio of the speeds of a motor boat and that of the current of water is 26:4. The boat goes certain distance against the current in 6 hrs. The time taken by the boat to come back is____

From a container full of milk, 10 liters (l) was drawn and replaced by water. This process is repeated one more time. The ratio of quantity of milk and water left in the container is 4:5. Then the capacity of the container is:

'A' can run 1km in 5 minutes 20 seconds and 'B' can run the same distance in 6 minutes. How many meters start can 'A' give 'B' in a kilometer race so that they finish the race together?

A man rows 15 km upstream in 5 hours and 25 km downstream in 5 hours each time, then the speed of the stream is

The remainder, when $5^{60}$ is divided by 7, is

In a game of 100 points, A can give 20 points to B and 28 points to C. How many points can B give C?

The value of $3^{18}(mod \space 4)$ is equal to

A swimmer whose speed in still water is 6 km/hr, swims between two points in a river and returns to the starting point. He took 20 minutes more to cover the distance upstream than downstream. If the speed of the stream is 3 km/hr, then the distance between the two points is:

In what ratio, water must be added to dilute honey costing ₹ 320 per liter so that the resulted syrup would be worth ₹ 280 per liter?

Three pipes A, B and C are installed to fill a tank. Pipes A and B opened together can fill the tank in the same time in which C can alone fill the tank. If pipe B can fill the tank 15 minutes faster than pipe A and 5 minutes slower than pipe C then the time required by pipe A to fill the tank alone is

The cost of type 1 rice is Rs. 20 per kg and type 2 rice is Rs. 30 per kg. If both Type 1 and Type 2 are mixed in the ratio 2:3, then the price per kg of the mixed variety is

In a kilometer race, A beats B by 50 meters or by 5 seconds, then the time taken by A to complete the race is

The least non-negative remainder, when $5^{61}$ is divided by 7, is

A man rows downstream 30 km and upstream 20 km. If he takes 5 hours to cover each distance, then the speed of stream is

Pipe A and B can fill a tank in 20 hours and 25 hours respectively, and pipe C can empty the full tank in 40 hours.If all the pipes are opened together, then how much time will be needed to make the tank full?

In what ratio should a shopkeeper mix two types of rice, one costing ₹20 per kg and another costing ₹40 per kg to get a rice variety costing ₹ 28 per kg?

A runs 3 times as fast as B. If A gives B a start of 30 meters, how far must the goal on the race course be so that A and B reach it at the same time?

The unit's digit of $12^{12}$ is equal to:

Two pipes A and B can fill a tank in 20 minutes and 30 minutes respectively. Both pipes A and B are opened together for some time and then pipe B is turned off. If the tank is filled in 15 minutes, then time for which the pipe B works is:

The non-negative remainder when $7^{30}$ is divided by 5 is

The speed of a motorboat in still water and that of the current of water is in a ratio of 27:5. The boat goes along the current from point A to point B in 3 hours 40 minutes. How much time will it take to come back from B to A?

A shopkeeper has 300 Kg millet, a part of which he sells at 10 % profit. The remaining quantity of millet was of poor quality, and he sold it at 5 % loss. In the whole transaction, he made a profit of 7 %. The quantity of the millet sold at 5 % loss is:

Two pipes can fill a cistern in 8 and 12 hours respectively. The pipes are opened simultaneously, and it takes 12 minutes more to fill the cistern due to leakage. If the cistern is full, what will be the time taken by the leakage to empty it?

The least non-negative remainder when $3^{128}$ is divided by 7 is:

If $X = 11$ and $Y = 3$, then $X \mod Y = (X + aY) \mod Y$ holds

A tub contains 60 litres of milk. From this tub, 6 litres of milk was taken out and replaced with water. This whole process was repeated further two more times. How much milk is there in the tub now?

A person can row a boat in still water at the rate of 5 km/hr. It takes him 4 times as long to row upstream of a river as to row downstream to cover same distance in the same river. The speed of flow of the stream is

Two runners, Ajay and Vijay complete a 600 m race in 38 seconds and 48 seconds respectively. By how many meters will Ajay defeat Vijay?

Three pipes A, B and C can fill a tank in 12 hours, 15 hours and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, in how many hours will the tank be full?

The least non-negative remainder when $2^{101}$ is divided by 5 is:

A person can row a boat at 5 km/hr in still water. If the speed of water current in a river is 1 km/hr, and it takes him 1 hour to row to a place and come back, how far off is the place?

A steamer can row at the speed of 16km/hr in still water. If the river is flowing at 8 km/hr and it takes 12 hours for a round trip, then the distance between the two places is:

The unit digit of $12^{12}$ is:

In what ratio a grocery shopkeeper mix two varieties of pulses worth Rs. 85 per kg and Rs. 100 per kg respectively, so as to get a mixture worth Rs. 92 per kg?

Pipe A can fill the tank 3 times faster than pipe B. If both pipes A and B running together can fill the tank in 15 minutes, then the time taken by B alone to fill the tank is:

In a 700 m race, the ratio of speeds of two participants A and B is 5:6. If A has a start of 150 m, then the distance by which A wins the race is:

A pipe A can fill a tank in 4 hours. There are two outlet pipes, B and C, from the tank which can empty it in 8 and 10 hours respectively. If all the three pipes are opened simultaneously, how long will it take to fill the tank?

In a game of 100 points, A can give B 20 points and C 28 points. How many points can B give C?

Ram can row a boat in still water at the rate of 6 km/hr. He finds that it takes him twice as long to row upstream of a river as to row downstream of the same river, then the speed of the current of the river is

If water is mixed with milk to gain 20% by selling the mixture at cost price. Then ratio of water to milk in mixture, is:

A container contains 100 liters of milk. From this container, 10 liters of milk is taken out and replaced by water. This process is repeated two more times.The amount of milk left in the container now is:

In a game of billiards, A can give B, 15 points in 60 and A can give C, 20 points in 60. How many points can B give C in a game of 90?

Pure milk costs Rs. 75 per litre. A milkman adds water to 28 liters of pure milk and sells the mixture at Rs. 60 per litre. How many liters of water does he add?

A boat takes 1 hour 30 minutes less to travel 36 km downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 km/hr, then the speed of the stream is:

The remainder when $2^{340}$ is divided by 341 is:

The average salary per head of the entire staff of a small factory including the managers and technicians is Rs.5750. The average salary per head of the manager is Rs. 20000 and that of technicians is Rs. 5000. If there are four managers, then the number of technicians in the factory is:

Two pipes A and B can fill a tank in 20 minutes and 30 minutes respectively. Both pipes A and B are opened together for some time and pipe B is turned off. If the tank is filled in 15 minutes, then after how many minutes pipe B is turned off?

In a 10 km race, A, B and C each run at uniform speed, get the first, second and third position respectively. If A beats B by 1 km and B beats C by 1 km, then, by how much distance A beat C?

A fisherman is rowing a boat. He takes 6 hours to row 48 km upstream whereas he takes 3 hours to go to the same distance downstream. Based on the above information, which of the following are correct? (A) His speed of rowing in still water is 10 km/hour. (B) The speed of the stream is 3 km/hour. (C) The average speed of the fisherman is 32/3 km/hour. (D) The speed of the stream is 4 km/hour. Choose the correct answer from the options given below:

A boat covers 32 km upstream and 36 km downstream in 7 hours. Also, it covers 40 km upstream and 48 km downstream in 9 hours. The speed of the boat in still water is:

In a 500 m race, the ratio of speeds of two participants, A and B, is 4:5 respectively. If A has a start of 180 m, then the distance by which A wins is:

Pipe A can fill a tank three times faster than pipe B. If both pipes A and B are running together, they can fill the tank in 12 minutes, then the time taken by pipe B alone to fill the tank is: