A sum of Rs. 5200 is lent out in two parts in such a way that the interest on one part at 10% for 5 years is equal to that on the other part at 9% for 6 years. The sum lent out at 9% is ?

A sum of Rs. 5200 is lent out in two parts in such a way that the interest on one part at 10% for 5 years is equal to that on the other part at 9% for 6 years. The sum lent out at 9% is ?
1). 2700
2). 1350
3). 2500
4). 1250

Now formula for simple interest can be given as

⇒ SI = (P × T × R)/100

Where,

SI = Simple Interest

P = Principal amount

T = Time Period

R = Rate of Interest

Let the principal lent at 10% be X, therefore the principal lent at 9% will be (5200 - X)

Now,

Interest on principal lent at 10% for 5 years = Interest on principal lent at 9% for 6 years

⇒ X × 5 × 10/100 = (5200 - X) × 6 × 9/100

⇒ 50X =280800 - 54X

⇒ 104X = 280800

⇒ X = Rs. 2700

∴ The amount of Rs. 2700 is lent at 10%

⇒ The amount lent at 9% = 5200 - X = 5200 - 2700 = Rs. 2500

∴ The amount lent at 9% = Rs. 2500

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