Question Bank  Arithmetic  Shashank Prabhu, CAT 100 Percentiler

Q25) A, B and C started a business by investing 1/2, 1/3rd and 1/6th of the capital respectively. After 1/3rd of the total time, A withdrew his capital completely and after 1/4th of the total time B withdrew his capital. C kept his capital for the full period. The ratio in which total profit is to be divided amongst the partners is
a. 1 : 2 : 1
b. 4 : 1 : 4
c. 2 : 1 : 2
d. 1 : 2 : 2

Q26) A person buys 18 local tickets for Rs. 110. Each first class ticket costs Rs. 10 and each second class ticket costs Rs. 3. What will another lot of 18 tickets in which the number of first class and second class tickets are interchanged cost?
a. 112
b. 118
c. 121
d. 124

Q28) The Maximum Retail Price (MRP) of a product is 55% above its manufacturing cost. The product is sold through a retailer, who earns 23% profit on his purchase price. What is the profit percentage (expressed in nearest integer) for the manufacturer who sells his product to the retailer? The retailer gives 10% discount on MRP.
A. 31%
B. 22%
C. 15%
D. 13%
E. 11%

Q29) A milkman mixed 20 L of water with 100 L of milk. He sold onefifth of the mixture and added as much water to the remaining mixture as the quantity he sold. Find the ratio of water and milk in the mixture now.
(a) 1:5
(b) 1:3
(c) 1:4
(d) 1:2

Q30) A and B started traveling simultaneously towards each other from two places which are 1260 km apart. They travel with the respective speeds of 130 kmph and 122 kmph. What is the total distance covered by them in the last one minute before they cross each other?
(a) 2.8 km
(b) 3.6 km
(c) 4.2 km
(d) 5.0 km

Q36) A child, playing at the balcony of his multistoried apartment, drops a ball from a height of 350 m. Each time the ball rebounds, it rises 4/5th of the height it has fallen through. The total distance travelled by the ball before it comes to rest is

Q39) A truck travelling at 70 km/hr uses 30% more diesel to travel a certain distance than it does when it travels at a speed of 50 km/hr. If the truck can travel 19.5 km/L of diesel at 50 km/hr, how far can the truck travel on 10 L of diesel at a speed of 70 km/hr?

Q41) Two farmers were cultivating wheat on their respective agricultural land in a village. Farmer A had an average production of 20 bushels from a hectare. Farmer B, who had 15 hectares of more land dedicated to wheat cultivation, had an output of 30 bushels of wheat from a hectare. If farmer B harvested 530 bushels of wheat more than farmer A, how many bushels of wheat did farmer A cultivate?
a. 50
b. 80
c. 160
d. 200

Q44) The work done by 4 men in 12 days is equal to the work done by 6 women in 10 days and is also equal to the work done by 8 children in 9 days. A man, a woman, and a child working together take 10 days to complete a particular job, in how many days will the same job be completed by 2 women and 5 children working together?

Q50) In an examination, the average marks obtained by students who passed was x%, while the average of those who failed was y%. The average marks of all students taking the exam was z%. Find in terms of x, y and z, the percentage of students taking the exam who failed.
a. (z  x)/(y  x)
b. (x  z)/(y  z)
c. (y  x)/(z  y)
d. (y  z)/(x  z)
e. (y  z)/(x  y)

Q51) Jugad Singh’s old Bajaj Chetak scooter had a leak in the petrol tank, and was always stuck in the second gear. This meant that he could only travel along at a steady 30 km per hour and managed a paltry 20 km per liter of petrol. Jugad had to start from his village, take CAT 2016 in Patiala and then ride back to his village. At the start of the journey he had exactly 10 liters of fuel in the tank. He knew though, that the fuel tank lost fuel at the rate of half a liter per hour. Just as he arrived home, the scooter stopped because it had run out of fuel. How far is Jugad’s village from his CAT center in Patiala?

Q56) By selling an article at a discount of 25%, a shopkeeper gets Rs. 16 less as profit than by selling it at 50/3% discount. If the cost of 12 articles is equal to the marked price of 8 articles, then find the cost price (in rupees) of each article.

Q61) Govind has 2 vessels of equal capacity. The first is filled to capacity with milk and the second if filled to onethird of the capacity with water. The second vessel is now filled to capacity using only the contents of the first vessel. Finally, this process is reversed and the first vessel is filled up to capacity. What is the ratio of milk and water in the first vessel now?

Q63) Hogwarts Express starts from London, King's Cross Station, Platform 9 3/4 and another Hogwarts Express starts from Hogsmeade which is 2160 km far from London. At some point during the journey, the two trains cross each other in 10 seconds. If the length of each of the two trains is 800 m, how much time would it have taken them to meet each other from the time they started their respective journeys?

Q64) 2 men do as much work as is done by 3 children in a day. 5 women do as much work as is done by 3 men in a day. If a man, a woman and a child are employed, it takes 10 days to finish the job. How many days will 2 children working together take to complete the job?

Q71) 10% of a vessel full of milk is drawn off and replaced with water. Then 10% of this mixture is drawn off and replaced with milk. 10% of the mixture is again drawn off and replaced with water. If the vessel now contains 199.1 litres of water, what is the volume of the vessel? (in litres)

Q76) Rani was sneaking candies from the fridge. On the way to her room she encountered her three sisters one after the other one, each of whom had to be given one third of the candies Rani had plus three more to get them promise that they wouldn't tell their mother. In the end, Rani was left with seven candies. How many did she take from the fridge?

Q79) A firm has tractors of four models, A, B, C, D. Four tractors (2 of model B and one each of models C and D) plough a field in two days. Two model A tractors and one model C tractor take three days to do this job. Three tractors one each of models A, B and C take four days to do the same task. How long will it take to do the job if a team is made up of four tractors of different models?

Q90) A milk merchant buys certain number of cans full of milk. If he sells milk at Rs. 13 per litre, he gains Rs. 333. But if he sells milk at Rs. 10 per litre, he loses Rs. 150. How many such cans did be buy, if the capacity of each can is 23 litres?

Q96) A train, 600 m long, starts from Pune to Jammu at 5:40 p.m. At the same time, another train, 350 m long, starts from Jammu to Pune on a parallel track. On the way, the train from Pune crosses a tunnel in 35 seconds while the train from Jammu crosses the same tunnel in 40 seconds. After crossing each other inside the tunnel, the trains reach Jammu and Pune 4 hours and 9 hours later respectively. What is the length of the tunnel?
a. 700 m
b. 450 m
c. 750 m
d. 1050 m