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…

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