A sum of Rs. 4,200 is lent out in two parts such that for 8 years the interest on one part at 10% p.a. is equal to the interest on the other part at 7% p.a. for 5 years. What is the second part?

Explanation

Let the first part be x, lent at 10% for 8 years.  

So, interest = (x × 10 × 8)/100 = 0.8x

Let the second part be (4200 − x), lent at 7% for 5 years.  

So, interest = [(4200 − x) × 7 × 5]/100 = (35/100)(4200 − x) = 0.35(4200 − x)

Since both interests are equal:

0.8x = 0.35(4200 − x)

Solve:

0.8x = 1470 − 0.35x  

0.8x + 0.35x = 1470  

1.15x = 1470  

x = 1278.26

So, second part = 4200 − 1278.26 = Rs. 2,921.74 ≈ Rs. 2,921

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