A sum of Rs. 2600 is lent out in two parts in such a way that the simple interest on one part at 10% per annum for 5 years is equal to that on another part at 9% per annum for 6 years. The sum lent out at 9% is

A sum of Rs. 2600 is lent out in two parts in such a way that the simple interest on one part at 10% per annum for 5 years is equal to that on another part at 9% per annum for 6 years. The sum lent out at 9% is
1). Rs. 500
2). Rs. 1000
3). Rs. 1250
4). Rs. 1350

Total amount is Rs. $2600$

Let the part given on $10%$ per annum is $= P$

Then sum lent at $9%$ per annum is $= 2600 – P$

S.I. on amount $P$ for $5$ years at $10% = (\frac{{P \times 10 \times 5}}{{100}})$

S.I. on amount $(2600 – p)$ for $6$ yr at $9% (= \frac{{\left( {2600\;-\;p} \right) \times 6 \times 9}}{{100}})$

Given, Both S.I. are equal:

$(\frac{{\left( {P \times 10 \times 5} \right)}}{{100}} = \frac{{\left( {2600\;-\;p} \right) \times 6 \times 9}}{{100}})$

$⇒ 50P = 140,400 - 54P$

$⇒ 104P = 140,400$

$⇒ P = 140,400/104 = 1350$

∴ Sum lent at $9%$ per annum is $= 2600 – 1350 = Rs. 1250$

10% for 5 years = 50%

9% for 6 years = 54%

50% of x = 54% of y

x/y = 54/50 = 27/25

52p = 2600

27p = 1350

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