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?

68,000

64,000

64,125

63,000

APEDIA

NTPC Graduate Tier 1

2025 • 09 Jun, 2025 • Shift-1

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 Answer

64,125

Variable Assignment: Let the monthly incomes of Seema and Darshan be algebraically represented as 7x and 8x respectively.Expenditure Equation Setup: Basic econo......

💡 Analysis & Explanation

Variable Assignment ▼

Let the monthly incomes of Seema and Darshan be algebraically represented as 7x and 8x respectively.

Expenditure Equation Setup ▼

Basic economic logic dictates that Expenditure equals Income minus Savings. Therefore, Seema's expenditure is (7x - 15000) and Darshan's expenditure is (8x - 9000). The problem states their expenditure ratio is 11:16. Thus, we format the equation: (7x - 15000) / (8x - 9000) = 11 / 16.

Solving for the Multiplier (x) ▼

Cross-multiplying the equation yields 16(7x - 15000) = 11(8x - 9000). Expanding the terms gives 112x - 240000 = 88x - 99000. Rearranging terms to isolate x results in: 24x = 141000, which calculates to x = 5875.

Total Expenditure Calculation ▼

The sum of their expenditures is (7x - 15000) + (8x - 9000) = 15x - 24000. Substituting our found value of x into this formula gives: 15(5875) - 24000 = 88125 - 24000 = 64125.

Conclusion ▼

The total combined expenditure amounts to ₹64125.

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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?