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Harshit invested 3/2 times the amount invested by Aditya in a coaching class. After 6 months, Aditya withdrew ¾ th of his capital while after 9 months, Harshit withdrew half of his capital. At the end of one year, profits made were equal to Rs. 1,17,800. What is the amount received by Harshit?  

Harshit invested 3/2 times the amount invested by Aditya in a coaching class. After 6 months, Aditya withdrew ¾ th of his capital while after 9 months, Harshit withdrew half of his capital. At the end of one year, profits made were equal to Rs. 1,17,800. What is the amount received by Harshit?   Correct Answer Rs. 79,800

Given:

Harshit invested 3/2 times the amount invested by Aditya in a coaching class.

After 6 months, Aditya withdrew ¾ th of his capital while after 9 months, Harshit withdrew half of his capital.

At the end of one year, profits made were equal to Rs. 1,17,800.

Concepts used:

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

Calculation:

Harshit invested 3/2 times the amount invested by Aditya in a coaching class.

Let capital invested by Aditya be x.

⇒ Capital invested by Harshit = 3x/2

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

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

After 9 months, Harshit withdrew half of his capital.

⇒ Net capital invested by Harshit = (9 × 3x/2) + 3 × {3x/2 – (1/2 × 3x/2)} = 63x/4

Ratio of net capital of Aditya and Harshit = 15x/2 ∶ 63x/4 = 10 ∶ 21

At the end of one year, profits made were equal to Rs. 1,17,800.

⇒ Amount of profits received by Harshit = 21/(21 + 10) × Rs. 1,17,800

⇒ Amount of profits received by Harshit = Rs. 79,800

∴ Harshit received profits equal to Rs. 79,800. 

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