Question:

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: Read the relations carefully.
The sentence has two links in it. "R got double than P" means R's share is twice P's share. "P who got double than Q" means P's share is twice Q's share. So Q has the smallest share and R the largest.
The smart move is to name the smallest share as the variable, because then the other two come out as whole multiples with no fractions.

Step 2: Write all three shares in one variable.
Let Q's share be \( x \) rupees.
Then P's share is \( 2x \), since P got double of Q.
Then R's share is \( 2 \times 2x = 4x \), since R got double of P.
So the shares of Q, P and R are in the ratio \( 1 : 2 : 4 \).

Step 3: Use the given difference.
The difference between R and Q is
\[ 4x - x = 3x \]
We are told this equals 3675, so
\[ 3x = 3675 \]
\[ x = 1225 \]
So Q got Rs. 1225, P got Rs. 2450 and R got Rs. 4900.

Step 4: Add up to get the total sum.
\[ \text{Sum} = x + 2x + 4x = 7x = 7 \times 1225 = 8575 \]
As a check, \( 1225 + 2450 + 4900 = 8575 \), and \( 4900 - 1225 = 3675 \), which matches the given difference.

Step 5: Look at the wrong options.
Option (A) 4900 is only R's share, not the total. It is the classic "stopped one step early" trap.
Option (D) 7350 equals \( 6x \), which you get by adding the ratio parts as \( 1+2+3 \) instead of \( 1+2+4 \), that is, by misreading "double" somewhere in the chain.
Option (C) 11025 equals \( 9x \), which comes from using shares in the ratio \( 1:2:6 \) or from multiplying 3675 by 3 instead of using the right total.
Only \( 7x = 8575 \) fits the ratio \( 1:2:4 \).

Final Answer:
The sum divided among the three was Rs. 8575.
\[ \boxed{\text{Rs. }8575} \]
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