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Question
On a certain sum of money, the difference between the compound interest for a year, payable half-yearly, and the simple interest for a year is Rs. 180/- Find the sum lent out, if the rate of interest in both the cases is 10% per annum.
Solution
Let principal p = Rs. 100; R = 10%; T = 1 year
SI = `[100 xx 10 xx 1]/100` = Rs. 10.
CI payable at every 6 months
So, R = `10/2` = 5%
I = `[100 xx 5 xx 1]/100`= Rs. 5
A = 100 + 5 = Rs. 105
For second year
P = Rs. 105
I = `[ 105 xx 5 xx 1]/100` = Rs. 5.25
Total compound interest = 5 + 5.25 = Rs. 10.25
Difference of CI and SI = 10.25 - 10 = Rs. 0.25
When difference in interest is Rs. 0.25, sum = Rs. 100.
If the difference is Rs. 1 then
sum = `100/0.25`
If the difference is Rs. = 180 then
sum = `100/0.25 xx 180` = Rs. 72,000.
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