4,800 is divided between A, B and C in such a way that the ratio of A's share to the joint share of B and C is 3 : 5 and C gets \(\frac{5}{7}\) of the joint share of A and B. What is the difference (in) between parts A and B?

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Question

This question was previously asked in

Punjab Police Constable Official Paper-I & II (Held On: 30 Jul, 2024 Shift 1)

Answer 1

Given:

Total amount = 4800

Ratio of A's share to (B+C)'s share = 3 : 5

C's share = \(\frac{5}{7}\) of (A+B)'s share

Formula Used:

Ratio and proportion

Calculation:

From the first ratio, A : (B + C) = 3 : 5

Total parts = 3 + 5 = 8

Value of 1 part = 4800 / 8 = 600

A's share = 3 × 600 = 1800

B + C = 5 × 600 = 3000

From the second condition, C = \(\frac{5}{7}\) (A + B)

C = \(\frac{5}{7}\) (1800 + B)

We know B + C = 3000, so C = 3000 - B

\(\Rightarrow\) 3000 - B = \(\frac{5}{7}\) (1800 + B)

\(\Rightarrow\) 7(3000 - B) = 5(1800 + B)

\(\Rightarrow\) 21000 - 7B = 9000 + 5B

\(\Rightarrow\) 21000 - 9000 = 5B + 7B

\(\Rightarrow\) 12000 = 12B

\(\Rightarrow\) B = 12000 / 12 = 1000

Difference between A and B = |A - B| = |1800 - 1000| = 800

The difference between parts A and B is 800.

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