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Aarti has lent some money to Bharti at 5% p.a. and Swati at 10% at the end of the year he has gain the overall interest at 8% p.a. in what ratio has he lent the money to Bharti and Swati ?


1. 3 : 2
2. 1 : 2
3. 2 : 1
4. 2 : 3
5. None of these

1 Answer

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Correct Answer - Option 4 : 2 : 3

Solution:

Given: Bharti has money at interest rate = 5%

Swati has money at interest rate = 10%

Overall interest rate gain by Aarti = 8%

Concept used: {Amount lent to Bharti × (rate/100)} + {Amount lent to Swati × (rate/100)} = {(Amount lent to Bharti + Amount lent to Swati) × (rate/100)}

Calculation: Let the money lent to Bharti is ‘x’ and money lent to Swati is ‘y’.

Then, {x × (5/100)} + {y × (10/100)} = {(x + y) × (8/100)}

⇒ (5x/100) + (10y/100) = (8x/100) + (8y/100)

⇒ (8x – 5x)/100 = (10y – 8y)/100

⇒ 3x = 2y

⇒ x/y = 2/3

∴ Aarti has lent the money to Bharti ad Swati in the ratio 2 : 3.

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