A sum of Rs. 2600 is lent out in two parts in such a way that the simp

1.	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% is1). Rs. 5002). Rs. 10003). Rs. 12504). Rs. 1350
Answer» 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

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% is1). Rs. 5002). Rs. 10003). Rs. 12504). Rs. 1350

Answer»

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

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