Question:easy

A sum was divided among P, Q & R. R got double than P who got double than Q. If the difference between the shares of Q and R is Rs. 3675.00, then the sum in rupees is

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Take Q's share as x. Then P is 2x and R is 4x, so R minus Q is 3x equal to 3675. The sum is 7x.
Updated On: Jul 17, 2026
  • 4900
  • 8575
  • 11025
  • 7350
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The Correct Option is B

Solution and Explanation

Step 1: Convert the wording into a ratio in one line.
R is twice P, and P is twice Q. Chaining these, R is four times Q. So writing the shares in the order Q, P, R gives the ratio
\[ Q : P : R = 1 : 2 : 4 \]
Ratios are handy here because the actual rupee amounts are unknown but their relative sizes are fixed.

Step 2: Attach the ratio to the known difference.
In ratio terms, the gap between R and Q is $4 - 1 = 3$ parts. That gap is worth Rs. 3675, so
\[ 1 \text{ part} = \frac{3675}{3} = 1225 \]
Every part of the ratio is therefore worth Rs. 1225.

Step 3: Count the total number of parts.
The whole sum is made of $1 + 2 + 4 = 7$ parts. So
\[ \text{Sum} = 7 \times 1225 = 8575 \]

Step 4: A shortcut worth remembering.
Since the difference covers 3 parts and the sum covers 7 parts, the sum is always $\frac{7}{3}$ of the given difference:
\[ \text{Sum} = \frac{7}{3} \times 3675 = 7 \times 1225 = 8575 \]
This avoids finding any individual share at all.

Step 5: Cross-check the individual amounts.
Q takes 1 part, Rs. 1225. P takes 2 parts, Rs. 2450, which is indeed double Q's. R takes 4 parts, Rs. 4900, which is indeed double P's. Their difference $4900 - 1225 = 3675$ matches, and their total $1225 + 2450 + 4900 = 8575$ matches too.

Step 6: Why the other numbers do not work.
Rs. 4900 is R's share alone, so it fails the word "sum".
Rs. 7350 is exactly twice the difference, which would need the sum to be 6 parts, meaning a ratio of $1:2:3$. That ignores the doubling from P to R.
Rs. 11025 is three times the difference, needing 9 parts, which no reading of the sentence supports.

Final Answer:
Seven parts at Rs. 1225 each give a total of Rs. 8575.
\[ \boxed{8575} \]
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