₹21,150 is distributed among A, B, and C. The share of A is $$\frac{4}{5}$$​ of the share of B, and the share of B is $$\frac{3}{4}$$​ of the share of C. After receiving their respective sums, C gives some money out of her share to A so that after the transfer, the ratio of the sums A and C have is 7 : 9. What part of her initial share did C transfer to A?

Correct option is B

Given:

Total amount = ₹21,150

A’s share = $$\frac{4}{5}$$​ of B’s share

B’s share = $$\frac{3}{4}$$​ of C’s share

After transfer, A : C = 7 : 9

Solution:
Let C’s share = x
Then B’s share =$$\frac{3}{4}$$​x

Then A’s share = $$\frac{4}{5} \times \frac{3}{4}x = \frac{3}{5}x$$​​
Total:

A + B + C $$= \frac{3}{5}x + \frac{3}{4}x + x = 21150$$​

​$$\left( \frac{12 + 15 + 20}{20} \right)x = 21150$$​

​$$\frac{47}{20}x = 21150$$​

x =$$\frac{21150 \times 20}{47} = 9000$$​

Now:

C’s initial share = ₹9000

A’s initial share =$$\frac{3}{5} \times 9000 = ₹5400$$​​

Let amount transferred from C to A = ₹t
After transfer:

A has ₹(5400 + t), C has ₹(9000 - t)
Given:

​$$\frac{5400 + t}{9000 - t} = \frac{7}{9}$$​​

9(5400 + t) = 7(9000 - t)

48600 + 9t = 63000 - 7t

16t = 14400

t = 900

Part of C's share transferred:

​$$\frac{900}{9000} = \frac{1}{10}$$ 

Alternate Method: 

​$$\frac 2{20}=\frac 1{10}$$​​