All Exams Test series for 1 year @ ₹349 only
Question

A man starting from a place P went x metre (x > 120 m) East before turning South. He went 40 m straight before turning to West. He went 60 m to reach a place Q. From Q he went 200 m North and reached a place R. If PR = 200 m, then what is x equal to?

This question was previously asked in
CDS 2 2025 Maths Question Paper (14-Sep-2025)
The correct answer is

150 m

Let the starting point P be the origin (0, 0). The man follows the following path:

1. He goes x metres East. His new position is (x, 0).

2. He turns South and goes 40 metres. His new position is (x, -40).

3. He turns West and goes 60 metres. His new position is (x - 60, -40). This is point Q.

4. From Q, he goes 200 metres North to reach point R. The new position is (x - 60, 160). This is point R.

The problem states that the distance from P to R is 200 metres. We can use the distance formula to find the distance PR:

PR² = (x - 60)² + (160)²

200² = (x - 60)² + 160²

Simplifying:

40000 = (x - 60)² + 25600

Subtract 25600 from both sides:

14400 = (x - 60)²

Taking the square root of both sides:

x - 60 = ±120

So, x = 180 or x = -60.

Since x > 120, the valid solution is:

x = 180

Thus, the correct value of x is 180 metres, but the correct answer given in your original statement is 150 metres, which seems to be a mistake in the provided question setup or options.

Was this answer helpful?

Similar Questions

  1. N is the smallest 5-digit number which when divided by 2, 2², 2³, ..., 2ⁿ leaves a remainder of 1. What is the value of n?

  2. What is the least number of complete years in which a sum of money put out at 20% compound interest (compounded annually) will be more than doubled?


Important Questions from Number System

  1. What is the value of 1 2 + 2 2 + 3 2 + ......21 2 ?

  2. Which sequence is correct to represent the hierarchical chain of number system?

    (Where N - Natural Numbers

    W - Whole Numbers

    Q - Rational Numbers

    Z - Integers)

  3. What must be added to 45680 to make it exactly divisible by 9?

  4. How many zeroes are there at the end of the following product? 

    1 x 5 x 10 x 15 x 20 x 25 x 30 x 35 x 40 x 45 x 50 x 55 x 60

  5. Let XYZ be a three-digit number, where (x + y + Z) is not a multiple of 3. Then (XYZ + YZX + ZXY) is not divisible by

Need Expert Advice?
Test Series
CDS img
Defence
UPSC CDS 2026 Mock Test Series
536 Tests 4 Tests Free
1643 Attempts
4.3(174)
English, Hindi
More Questions from CDS

Start Your Preparation with Prepp Mobile App

Download the app from Google Play & App Store
Download the app from Google Play & App Store
Prepp Mobile App