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Maths-

General

Easy

Question

What sum of money lent out at 6% for 2 years will produce the same interest as Rs. 1200 lent out at 5% for 3 years.

hint Hint:

Given that interest produced is same in both the cases. So equate two SI equations

The correct answer is: 1500 Rupees

Complete step by step solution:
We calculate simple interest by the formula, $S I equals fraction numerator P T R over denominator 100 end fraction$ …(i)
where P is Principal amount, T is number of years and R is rate of interest
Case Ⅰ
Let the sum of money = P
Here, we have $T equals 2 comma R equals 6 straight percent sign text and end text P equals ?$
On substituting the values in (i), we get $S I equals fraction numerator P cross times 2 cross times 6 over denominator 100 end fraction equals fraction numerator 12 P over denominator 100 end fraction$ …(ii)
Case Ⅱ
Here, we have $T equals 3 comma R equals 5 straight percent sign text and end text P equals 1200$
On substituting the values in (i), we get $S I equals fraction numerator 1200 cross times 3 cross times 5 over denominator 100 end fraction equals 18000 over 100$ …(iii)
It is given that the interest produced in both the cases is the same.
So, Equate (ii) and (iii)
On equating, we get $fraction numerator 12 P over denominator 100 end fraction equals 18000 over 100$
$not stretchy rightwards double arrow P equals 18000 over 12$
$not stretchy rightwards double arrow P equals 1500$ rupees.
Hence the sum of money P = 1500 Rupees

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