Question

A sum of Rs. 4000 is lent out in two parts, one at 8% simple interest and the other at 10% simple interest. If the annual interest is Rs. 352. The sum lent at 8% is

A) Rs. 2900 B) Rs. 2200 C) Rs. 2400 D) Rs. 3100

Answer 1

Answer:

₹2400

Step-by-step explanation:

average interest rate is = 352/4000*100

= 8.8 \ %

1st \\\\ 2nd

8 \ % \\\\\\ %

1.2 \\\\\\ 08

3\\\\\\\\\\ 2

( 3+2) = 4000

5=4000

1 = 800

3 = 800*3

₹2400

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Answer 2

$\sf\large\underline{Given:}$

A sum of Rs. 4000 is lent out in two parts, one at 8% simple interest and the other at 10% simple interest. If the annual interest is Rs. 352.

$\sf\large\underline{To\:Find:}$

• The sum lent at 8% is=?

$\sf\large\underline{Solution:}$

$\tt{\implies Let\:Sum\:_{(1st)}=x}$

$\tt{\implies Let\:Sum\:_{(2nd)}=4000-x}$

$\sf\small\underline{Calculation\:for\:1st\:SI:}$

$\tt{\implies SI\:_{(1st)}=\dfrac{P\times\:T\times\:R}{100}}$

• Here, P=x T=1 year R=8% ]

$\tt{\implies SI\:_{(1st)}=\dfrac{x\times\:1\times\:8}{100}}$

$\tt{\implies SI\:_{(1st)}=\dfrac{8x}{100}}$

$\sf\small\underline{Calculation\:for\:2nd\:SI:}$

$\tt{\implies SI\:_{(2nd)}=\dfrac{P\times\:T\times\:R}{100}}$

• Here, P=4000-x T=1 year R=10%]

$\tt{\implies SI\:_{(2nd)}=\dfrac{4000-x\times\:1\times\:10}{100}}$

$\tt{\implies SI\:_{(2nd)}=\dfrac{4000-x}{10}}$

• Now, calculate the sum lent 8% here]

$\tt{\implies SI\:_{(1st)}+SI\:_{(2nd)}=352}$

$\tt{\implies \dfrac{8x}{100}+\dfrac{4000-x}{10}=352}$

$\tt{\implies \dfrac{8x+40000-10x}{100}=352}$

$\tt{\implies \dfrac{-2x+40000}{100}=352}$

$\tt{\implies -2x+40000=35200}$

$\tt{\implies -2x=35200-40000}$

$\tt{\implies -2x=-4800}$

$\tt{\implies x=Rs.2400}$

$\sf\large{Hence,}$

$\tt{\implies The\:sum\:lent\:at\:8\%=Rs.2400}$

$\rm{\underbrace{Answer=Option-(C)}}$