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A sum of money is distributed among four people A, B, C and D in the ratio 4:7:9:3. If B gets ₹600 more than A, then how much more will C get than D?
₹800
₹600
₹1,200
₹1,400
₹1,200
Calculate the ratio difference: B - A = 7 - 4 = 3 units. Since 3 units = ₹600, 1 unit = ₹200. The target difference C - D = 9 - 3 = 6 units, which is 2 * 3 units (600 * 2 = 1200).
Ratio of money A:B:C:D = 4:7:9:3. B gets ₹600 more than A.
Value=Ratio×x
Calculate the ratio difference: B - A = 7 - 4 = 3 units. Since 3 units = ₹600, 1 unit = ₹200. The target difference C - D = 9 - 3 = 6 units, which is 2 * 3 units (600 * 2 = 1200).
Students often calculate the total sum of money first instead of finding the difference directly via ratio units, which is unnecessary and time-consuming.
Assign variables to ratios
Let the amounts received by A, B, C, and D be 4x, 7x, 9x, and 3x respectively.
A=4x,B=7x,C=9x,D=3x
Solve for unit x
Given that B gets ₹600 more than A, set up the equation 7x−4x=600. This simplifies to 3x=600, so x=200.
3x=600⟹x=200
Calculate C - D
Calculate the difference between C's and D's shares: 9x−3x=6x. Since x=200, the difference is 6×200=1200.
6x=6×200=1200
C is correct because the calculated difference of 6 units at ₹200 per unit results in ₹1,200.
This ratio-based shortcut is frequently used in Partnership, Profit & Loss, and Age problems to avoid solving for every individual variable.
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