Four friends A, B, C and D rented a bungalow and promised to share the rent as follows:

A : B = 8 : 15, B : C = 5 : 8, C : D = 4 : 5. What part of the rent C will pay?

Given:

A : B = 8 : 15

B : C = 5 : 8

C : D = 4 : 5

Formula used:

To find the share of C, we need to express all ratios in terms of a common variable and calculate the part of C.

Calculation:

First, express each ratio in terms of a common variable. Let’s assume:

A = 8k

B = 15k

From B : C = 5 : 8, we have:

B = 5m

C = 8m

Since B is common in both ratios, equate the two expressions for B:

15k = 5m

⇒ m = 3k

Now substitute m = 3k into the expression for C:

C = 8m = 8(3k) = 24k

From C : D = 4 : 5, we have:

C = 4n

D = 5n

Since C is common, equate the two expressions for C:

24k = 4n

⇒ n = 6k

Now substitute n = 6k into the expression for D:

D = 5n = 5(6k) = 30k

Sum of shares = A + B + C + D

= 8k + 15k + 24k + 30k = 77k

Part of the rent C will pay:

⇒ \(\dfrac{C}{A+B+C+D}\)

⇒ \(\dfrac{24k}{77k}\)

⇒ \(\dfrac{24}{77}\)

∴ The correct answer is option (1).