The ratio of the salaries of S to F is 2 : 3 and the ratio of their savings is 3 : 4. What is the ratio of their expenditures if their total savings are equal to the salary of S?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 8 : 13.
Let the salary of S be 2x and the salary of F be 3x.
Let the savings of S be 3y and the savings of F be 4y.
Total savings = 3y + 4y = 7y.
According to the given condition, total savings are equal to the salary of S.
⇒ 7y = 2x
⇒ y = 2x / 7
S's expenditure = 2x - 3y
F's expenditure = 3x - 4y
Substitute y = 2x / 7:
S's expenditure = 2x - 3(2x / 7)
⇒ 2x - 6x / 7
⇒ (14x - 6x) / 7
⇒ 8x / 7
F's expenditure = 3x - 4(2x / 7)
⇒ 3x - 8x / 7
⇒ (21x - 8x) / 7
⇒ 13x / 7
The ratio of their expenditures is (8x / 7) : (13x / 7).
⇒ 8 : 13