A’s income is equal to 125% of the income of B, while B’s savings are 120% of the savings of A. If the expenditure of B is 75% of the expenditure of A, then how much are B’s savings as a percentage of her expenditure?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 20%.
We know that,
Income = expenditure + savings
Now,
Let the income of B be 100.
Income of A = 125% of 100 = 125
Let the savings of A be x
Savings of B = 120% of x = 1.2x
Expenditure of A = 125 - x
Expenditure of B = 75% of (expenditure of A) = 75% of (125 - x) = 93.75 - 0.75x
Income of B = Savings of B + Expenditure of B
⇒ 100 = 1.2x + 93.75 - 0.75x
⇒ 100 = 0.45x + 93.75
⇒ x = 6.25/0.45
⇒ x = 13.89
Savings of B = 1.2x = 16.67
Expenditure of B = 93.75 - 0.75x = 83.43
Hence, required percentage = (Savings/Expenditure) × 100 = (16.67/83.43) × 100 = 20%