TheCATExam
Sign in

CAT 1996 — QA Question 25

Basics of TSD/ProportinalityEasy
Passage / Data

Direction: Answer the questions based on the following information.

A salesman enters the quantity sold and the price into the computer. Both the numbers are two-digit numbers. But, by mistake, both the numbers were entered with their digits interchanged. The total sales value remained the same, i.e. Rs. 1,148, but the inventory reduced by 54.

A man travels three-fifths of a distance AB at a speed 3a, and the remaining at a speed 2b. If he goes from B to A and return at a speed 5c in the same time, then

Answer & solution

  • A

    1a+1b=1c

  • B

    a + b = 99

  • 1a+1b=2c

  • D

    None of these

Solution

Let the total distance be x. So the man travels a distance 3x5 at a speed 3a. Therefore, total time taken to travel this distance = 3x(15a)=x(5a)

[time=distancespeed]

He then travels a distance 2x5 at a speed 2b. Hence, time taken to travel this distance = 2x(10b)=x(5b). So total time taken in going from A to B = x(5a)+x(5b). Now he travels from B to A and comes back. So total distance travelled = 2x at an average speed 5c.
Hence, time taken to return = 2x(5c).

Since the time taken in both the cases remains the same, we can write x5a+x5b=2x5c

Therefore, 1a+1b=2c.

CAT 1996 QA Q25: A man travels three-fifths of a distance AB at a speed 3a, and the remaining at a speed 2b. If he goes from B — Solution | TheCATExam