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CAT 1996 — QA Question 26

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 from A to B at a speed x km/hr. He then rests at B for x hours. He then travels from B to C at a speed 2x km/hr and rests for 2x hours. He moves further to D at a speed twice as that between B and C. He thus reaches D in 16 hr. If distances A-B, B-C and C-D are all equal to 12 km, the time for which he rested at B could be

Answer & solution

  • 3 hr

  • B

    6 hr

  • C

    2 hr

  • D

    4 hr

Solution

Total time taken by the man to travel from A to D = 16 hr and total distance travelled = 36 km. The time that he would have taken had he not rested in between will be (16 – x – 2x) = (16 – 3x). But this time should be equal to the addition of the times that he takes to travel individual segments. This is given as:

12x+122x+124x=844x=21x. Therefore, 21x= (16 - 3x).

So we get the equation 3x2 – 16x + 21 = 0. Solving this equation, we get x = 3 or x = 73. This should be the time for which he rested at B.

CAT 1996 QA Q26: A man travels from A to B at a speed x km/hr. He then rests at B for x hours. He then travels from B to C at a — Solution | TheCATExam