Question

Mike has a total amount of INR 2,70,000. He invested a part of it at the simple interest rate of 15% p.a. and
another part at 20% p.a.
If after 3 years he got a total interest of INR 1,39,500, what is the amount he invested at both the places?​

Answer 1

Given :

• Total amount = ₹2,70,000
• Time = 3 years
• Rate = 15% & 20%
• Total Intrest = ₹1,39,500

Let :

✪ For Rate = 15% p.a.

• Principal = P
• Interest = I

✪ For Rate = 20% p.a.

• Principal = P'
• Interest = I'

Formula used :

✪ I = P×r×t

Solution :

• P + P' = 270000
• P' = 270000 - P ...... equation 1

• I + I' = 139500.......... equation 2

✪ For Rate = 15%

➮ I = P ×(15/100)× 3

➮ I = 0.45 P ....... equation 3

✪ For Rate = 20%

➮ I' = P' × (20/100)×3

➮ I' = 0.6P' .......... equation 4

✪ Adding equation, 3 & 4 , we get;

➮ I + I' = 0.45P + 0.6P'

Putting value of (I+I') & P' from equation 2 & 1 respectively, we get;

➮ 139500 = 0.45P + 0.6(270000 - P)

➮ 139500 = 0.45P + 162000 - 0.6P

➮ 0.6P - 0.45P = 162000 - 139500

➮ 0.15P = 22500

➮ P = 22500 ÷ 0.15

➮ P = ₹ 1,50,000

✪ Putting value of P in equation 1, we get;

➮ P' = ₹2,70,000 - ₹1,50,000

➮ P' = ₹1,20,000

ANSWER :

✪ Amount invested in rate = 15% p.a. ➮ INR 1,50,000

✪ Amount invested in rate = 20% p.a. ➮ INR 1,20,000