# Question Bank - 100 Arithmetic Questions From Previous CAT Papers (Solved)

• Let speed of the slowest runner be x and fastest runner be 2x
Let d be the distance covered by the slowest runner in 5 min
Then the distance covered by the fastest runner in 5 min is (d + 1000) metre
d/x = (d + 1000)/2x
=> d = 1000 metre
fastest runner covers (d + 1000) = 2000 metre in 5 minute
therefore he needs 10 minute to cover 4000 metre

• If we start forming equations here, we are trapped!

If you increase and decrease by the same percentage (say x) then the final result will be always lesser than than the initial value (net change is -x^2/100%). So to get the same result the increase percentage should be greater than the decrease percentage. Answer is p > q

Note - Number of years doesn't matter here. So it would be easy to just take one year and observe the trend. For example, let say he had 100 goats at the beginning and increased by 25%, to make the final count as 125. Now to bring it back to 100, we have to decrease by 20%. 25% > 20%

• Let d = distance of race.
Between A's finish and B's finish, B runs 12 meters while C runs 10 meters.
B's rate to C's rate = 6/5.
When B finishes, he is 8 meters ahead of C.
6/5 = d/(d-8)
d = 48 meters

• First cycle :
P(1 - x/100)(1 + x/100) = P - 441
so (x^2/100) = 441/P -- (1)

Second cycle :
(P - 441) (1 - x^2/100) = 1944.81 -- (2)

From (1) & (2)
(P - 441) (1 - 441/P) = 1944.81
(P - 441)(P - 441) = 1944.81P
P^2 - 2826.81P + 194481 = 0
P = 2756.25

• @master_shifu ...IS their any other way to solve this question?

• @deepalis727

Work with ratios

Ratio of speed of N & S = 4 : 1
=> Ratio of time taken by N & S = 1 : 4
Total time taken = 1 hour
Time taken by N to cover the distance AB = 1/5 hour = 12 minutes
Time taken by S to cover the distance AB = 4/5 hour = 48 minutes
When the train was late by 20 minutes, total time available = 40 minutes
N doubled the speed, so time taken to cover distance AB = 12/2 = 6 minutes
So, S should cover the distance in 40 - 6 = 34 minutes
ratio = 6 : 34 = 1 : 6 (approx)

• @master_shifu
Can we not calculate the average speed by adding the total distance, i.e 9000 kms and then adding the total time taken , i.e. 25 hours + 24 hours + 1.55(halt in India) and then dividing those figures. Total distance/total time?

• @master_shifu In 19 th question CAT 2002 in arithmetic, the answer comes is 43.5

• @master_shifu total time taken would be (5+17.5+20) = 42.5

• @swati-jha Thanks Swati. Corrected the solution.
Mistake was in distance values and is now clean, hopefully :)
Happy learning!

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