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Question
A sum of money amounts to ₹ 2,240 at 4 % p.a., simple interest in 3 years. Find the interest on the same sum for 6 months at 3`(1)/(2)`% p.a.
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Solution
Let P = ₹ 100
S.I. = `"PRT"/(100)`
= ₹ `(100 xx 4 xx 3)/(100)`
= ₹ 12
A = P + S.I.
= ₹ 100 + ₹ 12
= ₹ 112
If A is ₹ 112 then P is ₹ 100
If A is ₹ 1 then P is ₹`(100)/(112)`
If A is ₹ 2,240 then P be `(100)/(112) xx 2,240`
= ₹ 100 x 20
= ₹ 2,000
So, principal is ₹ 2,000
Now, for second case
P = ₹ 2,000
Time = 6 months = `(1)/(2)"year"`
R = `3(1)/(2) = (7)/(2)`% p.a.
2,000 x `(7)/(2) xx (1)/(2)`
∴ S.I. = ₹`(2,000 xx (7)/(2) xx (1)/(2))/(100)`
= ₹ `(2,000 xx 7 xx 1)/(100 xx 2 xx 2)`
= ₹ `(20 xx 7)/(4)`
= ₹ 35.
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