CAT Exam Numerical Ability

26 friends, A to Z, are running a 10 km race to raise awareness about cancer. The race is being run along the 100 m perimeter of a basketball court.
All 26 start from the same point at the same time and run in the same direction. Their speeds are in an Arithmetic progression, with A being the fastest and Z being the slowest.
A overtakes Z for the first time, 20 seconds after the start of the race. M takes 52 minutes 5 seconds to complete the race.
How many seconds after the start of the race, will all 26 be at the starting point together?

Read Solution (Total 1)

let speed of Z is z. difference is d...speed of M is z+13d=10000/3125=3.2 m/s. (z+25d)20-z*20=100. d=.2. z=.6. Now 100/.2=500 s. Ans is 500s
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CAT Other Question

Imagine a conveyor belt, with tins placed at regular intervals onto the belt at one end, moving along at a steady rate towards a labeling machine at the far end. A rabbit starts from a tin at the beginning of the belt and steadily jumps from tin to tin, finally jumping off immediately before the labeling machine.
When the rabbit jumps at a rate of one jump per second he arrives at the labeling machine in 20 jumps but if he speeds up and manages two jumps per second he can fit in 32 jumps before the end of the line.

How many tins are there on the line ? Ajay went to the market to buy a total of 90 apples , oranges and bananas . HE bought an equal number of apples and bananas .

The ratio of the number of apples and oranges he bought is 5:2

If the price of each was equal to that of each apple ,he could hav skipped the purchase of bananas and instead purchased the same number of apples and oranges as he actually bought for the same total amount .

If the prices r all integers , find the minimum possible total expenditure he could hav incurred in RS.