2021 CSAT, all questions

UPSC Prelims 2021 · CSAT

Question 29: Basic Numeracy

A person X from a place A and another person Y from a place B set out at the same time to walk towards each other. The places are separated by a distance of 15 km. X walks with a uniform speed of 1·5 km/hr and Y walks with a uniform speed of 1 km/hr in the first hour, with a uniform speed of 1·25 km/hr in the second hour and with a uniform speed of 1·5 km/hr in the third hour and so on. Which of the following is/are correct ?

  1. 1.They take 5 hours to meet.
  2. 2.They meet midway between A and B.

Select the correct answer using the code given below :

a1 only
b2 only
cBoth 1 and 2
dNeither 1 nor 2

AnswerUPSC’s answer is (c).

X covers 1.5 km each hour. Y's speeds rise by 0.25 each hour: 1, 1.25, 1.5, 1.75, 2. After 5 hours X has walked 5 × 1.5 = 7.5 km and Y has walked 1 + 1.25 + 1.5 + 1.75 + 2 = 7.5 km, which add up to 15 km, so they meet after 5 hours. Four hours gives only 6 + 5.5 = 11.5 km, too little. Each has walked 7.5 km, half the distance, so they meet midway. Remember: sum the arithmetic progression of Y's hourly distances and compare totals each hour.

  • 1. After 5 hours X has walked 7.5 km and Y 7.5 km, a total of 15 km.
  • 2. Each has walked 7.5 km, half of 15 km, so the meeting point is midway.

How you could have got this

  1. If you were sure statement 1 is correct, (b) and (d) go: each of them leaves 1 out.

    What you needed to know: After 5 hours X has walked 7.5 km and Y 7.5 km, a total of 15 km.

  2. Then, if you were sure statement 2 is correct, (a) goes: it leaves 2 out.

    What you needed to know: Each has walked 7.5 km, half of 15 km, so the meeting point is midway.

Only (c) is left. This one needs every statement.

Which options go is worked out from UPSC’s key and the options, not by a model.

Why each option is right or wrong
  • (a) Statement 1 is true, but 2 is also true since each walks 7.5 km.
  • (b) Statement 2 is true, but 1 is also true: they meet after 5 hours.
  • (c) Right: after 5 hours each has walked 7.5 km, so they meet midway.
  • (d) Both statements hold, so this fails.

Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.

Practise this paper timedPrevious questionNext question

Source: UPSC, Civil Services (Preliminary) Examination 2021, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.