The ratio of incomes of C and D is 3:4, the ratio of their expenditures is…

2025

The ratio of incomes of C and D is 3:4, the ratio of their expenditures is 4:5. Find the ratio of their savings if the savings of C is one fourth of his income ?

  1. A.

    7/19

  2. B.

    11/19

  3. C.

    12/19

  4. D.

    19/12

Attempted by 16 students.

Show answer & explanation

Correct answer: C

Concept: When two ratios are given for the same pair of quantities (here, incomes and expenditures) using different scaling constants, express each quantity in terms of those constants, then use the one additional numeric condition given in the question to relate the constants — this converts a two-ratio setup into a single combined ratio.

Working:

  1. Let the incomes of C and D be 3x and 4x (ratio 3 : 4).

  2. Let the expenditures of C and D be 4y and 5y (ratio 4 : 5).

  3. Savings = Income − Expenditure, so Savings of C = 3x − 4y and Savings of D = 4x − 5y.

  4. Given: Savings of C = ¼ × Income of C, so 3x − 4y = ¼(3x) = ¾x.

  5. Solving: 4y = 3x − ¾x = 9x/4, so y = 9x/16, i.e. x : y = 16 : 9.

  6. Substituting x = 16, y = 9: Savings of C = ¾x = 12; Savings of D = 4x − 5y = 64 − 45 = 19.

  7. Ratio of savings of C to D = 12 : 19.

Cross-check: With x = 16, y = 9: incomes are 48 and 64 (ratio 3 : 4 ✓), expenditures are 36 and 45 (ratio 4 : 5 ✓), and C's savings 12 is exactly ¼ of C's income 48 ✓ — confirming the ratio 12 : 19.

Reference (handwritten working):

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