# Tina invested 5/4 times the amount invested by Aman in a startup. After 6 months, Aman withdrew ¾ th of his capital while after 9 months, Tina withdre

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Tina invested 5/4 times the amount invested by Aman in a startup. After 6 months, Aman withdrew ¾ th of his capital while after 9 months, Tina withdrew half of her capital. At the end of one year, profits made were equal to Rs. 1,10,000. What is the amount received by Tina?

1. Rs. 80,000
2. Rs. 40,000
3. Rs. 70,000
4. Rs. 50,000

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Correct Answer - Option 3 : Rs. 70,000

Given:

Tina invested 5/4 times the amount invested by Aman in a startup.

After 6 months, Aman withdrew ¾ th of his capital while after 9 months, Tina withdrew half of her capital.

At the end of one year, profits made were equal to Rs. 1,10,000.

Concepts used:

Net capital = Time for which capital is invested × capital invested

Calculation:

Tina invested 5/4 times the amount invested by Aman in a startup.

Let capital invested by Aman be x.

⇒ Capital invested by Tina = 5x/4

After 6 months, Aman withdrew ¾ th of his capital.

⇒ Net capital invested by Aman = (6 × x) + 6 × {x – (3x/4)} = 6x + (3x/2) = 15x/2

After 9 months, Tina withdrew half of her capital.

⇒ Net capital invested by Tina = (9 × 5x/4) + 3 × {5x/4 – (1/2 × 5x/4)} = 105x/8

Ratio of net capital of Aman and Tina = 15x/2 ∶ 105x/8 = 60 ∶ 105 = 4 ∶ 7

At the end of one year, profits made were equal to Rs. 1,10,000.

⇒ Amount of profits received by Tina = 7/(4 + 7) × Rs. 1,10,000

⇒ Amount of profits received by Tina = Rs. 70,000

Tina received profits equal to Rs. 70,000.