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Ayush’s father gave Rs. 20,000 to Ayush.  Ayush lent some money to Arnab for 2yr at 20 % simple interest. And remaining money to Ravish for the same time but at the interest rate of 24 %. After 2 years, interest received from Arnab was Rs. 729 more as interest received from Ravish. Find the amount of money which Ayush lent to Ravish.
1. 16524.5
2. 15000
3. 14625.5
4. 8,262.5

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Correct Answer - Option 4 : 8,262.5

Given:

Total amount with Ayush = Rs. 20000

Rate % for Arnab = 20 %

Rate % for Ravish = 24 %

Time = 2 years

Difference in interest between Arnab and Ravish = Rs. 729

Formula used:

Simple Interest = Principal × Rate/100 × time

Calculation:

Let the money lent to Arnab be ‘a’

Then, money lent to Ravish will be ’20,000 – a’

⇒ Simple interest for Arnab = a × 20/100 × 2

⇒ Simple interest for Arnab = 2a/5

⇒ Simple interest for Ravish = (20,000 – a) × 24/100 × 2

⇒ Simple interest for Ravish = (20,000 – a)12/25

According to the question,

SI from Arnab – SI from Ravish = Rs. 729

⇒ 2a/5 – (20,000 – a)12/25 = 729

⇒ 2a/5 – 9,600 + 12a/25 = 729

⇒ 22a/25 – 9,600 = 729

⇒ 22a/25 = 10,329

⇒ a = 10,329 × 25/22

⇒ a = 11,737.5

Amount lent to Ravish = 20,000 – 11,737.5 = Rs. 8,262.5

∴ The amount of money which Ayush lent to Ravish is Rs. 8,262.5

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