CAT Question Bank  Arithmetic

Q23) A circular park has four entrance gates such that the pathways joining the opposite gates are perpendicular at the center. Suresh and Ramesh held a race among them. The task was to start from a gate and reach back there touching all the gates exactly once. Suresh being a smarter kid completed the race by choosing the smallest possible path. Ramesh reached the opposite gate by covering the distance through the circumference of the path but seeing himself lagging behind, took the smallest path thereafter. Incidentally they reached the end point at the same time. If Suresh’s speed is 350m/min, Ramesh’s speed would have been approximately:
a) 370m/min
b) 380m/min
c) 390m/min
d) 400m/min

Q24) A person who has a certain amount with him goes to market. He can buy 50 oranges or 40 mangoes. He retains 10% of the amount for taxi fares and buys 20 mangoes and of the balance he purchases oranges. Number of oranges he can purchase is?

Q25) A software engineer agrees to work one year for an employer for 45,000 Rs and a laptop. The engineer realizes after 7 months that he was underpaid and he quits. The employer gave him 20,000 Rs and the laptop. How much was the laptop worth?

For an year he was offered 45000 and laptop
He left job after 7 months and got 20,000 and laptop.
Had he continued working for 5 more months, he would have got 25000 extra. (45000  20000)
So 5000 is the payment per month.
For a whole year payment would be 12 x 5000 = 60000
60000 = 45000 + laptop
laptop = 15000.

Q26) Out of 200 fish in an aquarium, 99% are red. How many red fishes must be removed in order to reduce the percentage of red fishes to 98%?

It is given that we have total 200 fishes out of which 99% are red fish. Means we have 198 red fish and 2 non red fish.
After the change, 98% are red fish and remaining 2% are non red fish. As there was no change in the non red fish count, 2 non red fish we had now account for 2%.
So, 2% = 2 fish
100% = 100 fish.
Red fish (98%) = 98
Change in red fish = 198  98 = 100
So 100 red fish removed in the process

Q27) The cost of a certain diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1:2:3:4. When the pieces were sold, the merchant got Rs. 70,000 less. Find the original price of the diamond.

Q28) A trader cheats both his supplier and customer by using faulty weights. when he buys from the supplier,he takes 10% more than the indicated weight. when he sells to his customer, he gives 10% less than the indicated weight, and adds stones so that they form 20% of the mixture .if he sells at cost price,what is the profit percent?

Q29) Ajay and Parag simultaneously start running from A and B respectively towards points B and A respectively with constant speed. On reaching points B and A respectively, they immediately turn back and run towards their starting points with same speed. This process continues. On their way, they meet each other at a point 360 m away from A during their first meeting and at a point 400 m away from B in their second meeting. What is the distance of their third meeting point from point B?

Q30) P and Q run on a circular track of 100m. Speed of P is 250 m/s and that of Q is 400 m/s. In how many points on a circular track will they meet if they start simultaneously from the same point, in the same direction?