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