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A sum of Rs. 46,800 is divided among A, B, C and D in such a way that the ratio of the combined share of A and D to the combined share of B and C is 8 ∶ 5. The ratio of the share of B to that of C is 5 ∶ 4. A receives Rs. 18,400. If x is the difference between the shares of A and B and y is the difference between the shares of C and D, then what is the value of (x – y) (in Rs.)?

A sum of Rs. 46,800 is divided among A, B, C and D in such a way that the ratio of the combined share of A and D to the combined share of B and C is 8 ∶ 5. The ratio of the share of B to that of C is 5 ∶ 4. A receives Rs. 18,400. If x is the difference between the shares of A and B and y is the difference between the shares of C and D, then what is the value of (x – y) (in Rs.)? Correct Answer 6000

Given:

Total sum = Rs. 46,800

The ratio of the combined share of A and D to the combined share of B and C = 8 : 5

The ratio of the share of B to that of C = 5 : 4

A receives = Rs. 18,400

Calculation:

The ratio of the combined share of A and D to the combined share of B and C = 8 : 5

⇒ (A + D) : (B + C) = 8 : 5

The ratio of the share of B to that of C = 5x : 4x

⇒ (5x + 4x) = 9x

Now,

We multiply the combined share of A and D and the combined share of B and C by 9

⇒ (8 : 5) × 9

⇒ 72 : 45

The share of A and D = 72 units

The share of B and C = 45 units

According to the question

The ratio of the share of B to that of C

⇒ 9x = 45 units

⇒ x = 5 units

The share of B = 5x = (5 × 5) = 25 units

The share of C = 4x = (4 × 5) = 20 units

Now,

The combined sum of A to D and B to C = (72 + 45) units = 117 units

⇒ 117 units = 46,800

⇒ 1 unit = (46,800/117)

⇒ Rs. 400

Now,

B receives = (25 × 400) = Rs. 10,000

C receives = (20 × 400) = Rs. 8,000

Now,

D receives = Total sum – (A + B + C)

⇒ 46,800 – (18,400 + 10,000 + 8,000)

⇒ 46,800 – 36,400

⇒ Rs. 10,400

⇒ D receives = Rs. 10,400

Now,

x is the difference between the shares of A and B = Rs. (18,400 – 10,000)

⇒ x = Rs. 8,400

y is the difference between the shares of C and D = Rs. (10,400 – 8000)

⇒ y = Rs. 2,400

Now,

The value of (x – y) = Rs. (8,400 – 2,400)

⇒ Rs. 6,000

∴ The required value is Rs. 6000

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