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An equal sum is invested for seven years in Scheme A offering simple interest at x% p.a. and in scheme B for two years offering compound interest at 10% p.a.(compounded annually). The interest earned from scheme A is thrice of the interest earned from scheme B. Had the rate interest been (x-4)% simple interest per annum in scheme A, the difference in the interest earned from both the schemes would have been Rs. 700. What was the sum invested in each of the schemes?
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Explanation:
Investment in each scheme = Rs. y
S.I.
= Principal×Time×Rate\100
C.I. = P [(1+R\100)^T−1]
Case I,
y×7×x\100=3y[(1+10\100)^2−1]
=> 7x\100=3[((11\10)^2−1]
=> 7x\100=3[(121\100−1]
=> 7x\100=3×21\100
=> x = 9% per annum
Case II,
New rate of S.I.
= 5% per annum
According to the question,
y×5×7\100−y[(1+10\100)^2−1]
= 700
=> 35y\100−y(121\100−1) = 700
=> 35y\100−21y\100 = 700
=> 14y\100 = 700
=> y = 700×100\14
= Rs.5000