Anil donates 30% of his income to a school and deposits 70% of the remainder…
2021
Anil donates 30% of his income to a school and deposits 70% of the remainder in his bank. If he has ₹9765 now, then what is the income of Anil?
- A.
₹45,600
- B.
₹45,500
- C.
₹46,500
- D.
₹46,000
Attempted by 289 students.
Show answer & explanation
Correct answer: C
Concept
When a percentage is taken “of the remainder,” the base shrinks at each stage. If you keep a fraction f of a quantity and then keep a fraction g of what is left, the final amount is the product f × g of the original — the successive fractions multiply, they do not add or subtract.
Application
Let the income be x.
Donating 30% leaves the remainder = 70% of x = 0.70x.
Depositing 70% of that remainder means he keeps 30% of it, so the amount he holds now = 0.30 × 0.70x = 0.21x (i.e. 21% of his income).
Set 0.21x = ₹9,765, so x = 9,765 ÷ 0.21 = ₹46,500.
Cross-check
21% of ₹46,500 = 0.21 × 46,500 = ₹9,765, which matches the amount he has now. So the income is ₹46,500.