The ratio of incomes of Seema and Darshan is 7 : 8. They save ₹15,000 and ₹9,000, respectively. If the ratio of their expenditures is 11 : 16, then what is the total expenditure (in ₹) of Seema and Darshan?

Correct option is C

Given:

The ratio of incomes of Seema and Darshan = 7 : 8

Savings of Seema = ₹15,000

Savings of Darshan = ₹9,000

The ratio of their expenditures = 11 : 16

Formula used:

Income = Savings + Expenditure

Solution:

Let Seema's expenditure be 11x and Darshan's expenditure be 16x (as per the ratio 11 : 16).

Seema's income = 15,000 + 11x
Darshan's income = 9,000 + 16x

As the ratio of their incomes is 7 : 8, we have:

​$$\frac{{(15,000 + 11x)}}{{(9,000 + 16x)}} = \frac{7}{8}$$​​

8(15,000 + 11x) = 7(9,000 + 16x)

120,000 + 88x = 63,000 + 112x

120,000 - 63,000 = 112x - 88x

57,000 = 24x

x = 2,375

Seema's expenditure = 11x = 11 × 2,375 = ₹26,125
Darshan's expenditure = 16x = 16 × 2,375 = ₹38,000

Total expenditure = Seema's expenditure + Darshan's expenditure

Total expenditure = ₹26,125 + ₹38,000 = ₹64,125