The ratio of incomes of C and D is 3:4. The ratio of their expenditure is…
2023
The ratio of incomes of C and D is 3:4. The ratio of their expenditure is 4:5.Find the ratio of their savings if the savings of C is one fourths of his income ?
- A.
7/19
- B.
11/19
- C.
12/19
- D.
19/12
Attempted by 15 students.
Show answer & explanation
Correct answer: C
Answer: 12/19 is the ratio of the savings of C and D.
Let the incomes of C and D be 3x and 4x, and their expenditures be 4y and 5y.
Given that C's saving is one-fourth of his income: 3x - 4y = (1/4)·3x. Multiply both sides by 4: 12x - 16y = 3x ⇒ 9x = 16y ⇒ x/y = 16/9.
Compute savings using x/y = 16/9: C's saving = 3x - 4y = (3·16/9)y - 4y = (48/9 - 36/9)y = 12/9 y = 4/3 y.
D's saving = 4x - 5y = (4·16/9)y - 5y = (64/9 - 45/9)y = 19/9 y.
Ratio of savings C:D = (4/3 y) : (19/9 y) = (4/3)·(9/19) = 12/19.