# Q. A person buys three articles P, Q and R for ₹ 3,330. If P costs 25% more than R and R costs 20% more than Q, then what is the cost of P?

a) ₹ 1,000

b) ₹ 1,200

c) ₹ 1,250

d) ₹ 1,350

Correct answer: d) ₹ 1,350

#### Question from UPSC Prelims 2024 CSAT

**Explanation : **

## THE COST OF P

Given:

– R costs 20% more than Q

– P costs 25% more than R

– Total cost (P + Q + R) = ₹3,330

**STEP 1: EXPRESS ALL COSTS IN TERMS OF Q**

Cost of Q = Q

Cost of R = Q + 20% of Q = 1.20Q

Cost of P = R + 25% of R = 1.25 × 1.20Q = 1.50Q

**STEP 2: FORM TOTAL COST EQUATION**

P + Q + R = 3,330

1.50Q + Q + 1.20Q = 3,330

3.70Q = 3,330

**STEP 3: SOLVE FOR Q**

Q = 3,330 ÷ 3.70

Q = 900

**STEP 4: CALCULATE P**

P = 1.50 × Q

P = 1.50 × 900

P = 1,350

ANSWER: P costs ₹1,350