The ratio of P, Q and R is 3 : 5 : 8 respectively. If their sum is 400, then…
2021
The ratio of P, Q and R is 3 : 5 : 8 respectively. If their sum is 400, then what is the difference between P and R?
Answer: A. 125 — Concept: To divide a total quantity in a given ratio, add the ratio terms to get the total number of equal parts, then divide the total by that sum to find…
- A.
125
- B.
75
- C.
100
- D.
50
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Correct answer: A
Concept: To divide a total quantity in a given ratio, add the ratio terms to get the total number of equal parts, then divide the total by that sum to find the value of one part; multiplying each ratio term by this value gives every individual share.
The ratio of P, Q and R is 3 : 5 : 8, so the total number of parts = 3 + 5 + 8 = 16.
Since P + Q + R = 400, the value of one part = 400 ÷ 16 = 25.
P = 3 × 25 = 75, Q = 5 × 25 = 125, and R = 8 × 25 = 200.
Difference between P and R = R − P = 200 − 75 = 125.
Cross-check: the difference can also be found directly from the ratio units — R's unit (8) minus P's unit (3) is 5 units, and 5 × 25 = 125, the same result. Also, P + Q + R = 75 + 125 + 200 = 400, matching the given total.
Hence, the difference between P and R is 125.