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David invested some money at the rate of 12% p.a. simple interest for 1 year. Out of the total money received
after 1 year, he donated 3 11.520 which is 200% of the interest received on the invested amount. He invested
the remaining amount for 2 years at the rate of 25% compound interest (compounded annually). Find the total
amount which lie will get after 2 years.
Step-by-step explanation:
Answer
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Suppose the person invested Rs x at the rate of 12% simple interest and Rs y at the rate of 10% simple interest. Then,
Yearly interest =10012x+10010y
∴10012x+10010y=130
⇒12x+10y=13000
⇒6x+5y=6500 .(i)
In the invested amounts are interchanged, then yearly interest increased by Rs 4.
∴10010x+10012y=134
⇒10x+12y=13400
⇒5x+6y=6700 ..(ii)
Subtracting equation (ii) from equation (i), we get
x−y=−200 .(iii)
Adding equation (ii) and (i), we get
11x+11y=13200
⇒x+y=1200 ..(iv)
Adding equations (iii) and (iv), we get
2x=1000⇒x=500
Putting x=500 in equation (iii), we get y=700
Thus, the person invested Rs 500 at the rate of 12% per year and Rs 700 at the rate of 10% per year.