​Total monthly income of A, B and C is ₹1,02,720. A, B and C save 20%, 10% and 25%, respectively of their incomes. If the ratio of their monthly expenditures is 3 : 4 : 5, then what is the sum (in ₹) of monthly incomes of A and C?

Correct option is A

Given:
Total income of A, B, C = ₹1,02,720
Savings: A = 20%, B = 10%, C = 25%
Expenditure ratio = 3 : 4 : 5
​Formula Used:
Income = Expenditure + Savings
Expenditure = (100% – Saving%) of Income
Income = $$\frac{\text{Expenditure}}{1 - \frac{\text{Saving \%}}{100}}$$​​
Solution:
Expenditure ratio given:
A : B : C = 3 : 4 : 5
Saving % for each:
A = 20% → spends 80% → $$\frac{3}{80\%} = 3 \times \frac{5}{4}=\frac{15}{4}$$​

B = 10% → spends 90% → $$\frac{4}{90\%}= 4 \times \frac{10}{9} = \frac{40}{9}$$​

C = 25% → spends 75% → $$\frac{5}{75\%} = 5 \times \frac{4}{3} = \frac{20}{3}$$​

Income ratio (A : B : C) = $$\frac{15}{4} \times 36 : \frac{40}{9} \times 36 : \frac{20}{3} \times 36$$

​​Income ratio (A : B : C) = 27 : 32 : 48

Total parts = 27 + 32 + 48 = 107 units
Each part = $$\frac{1,02,720}{107} = 960$$​​

Income of A =  $$960 \times 27 = ₹25920$$​​
Income of C =  $$960 \times48 = ₹46,080$$​​
Sum of incomes of A and C = 25,920 + 46080 = ₹72,000
Thus, the correct option is (a) ₹72,000