Question

Kamal and anand each lent the same sum of money for 2 years at 5% at simple interest and compound interest respectively . Anand received 15 Rs more than Kamal.Find the amount lent by each and the interest. (USING VARIABLE)

Answer 1

Given that:-

• Kamal and anand each lent the same sum of money for 2 years at 5% at simple interest & compound interest.

• Anand received 15 Rs more than Kamal.

To find:-

• Amount.

• Interest.

Solution:-

________________________

▪For kamal,

We have S.I = $\tt{\frac{PNR}{100}}$

$\implies$ $\tt{\frac{P\times2\times5}{100}}$

$\implies$ $\tt{\frac{10P}{100}}$ = 0.1P

▪For Anand,

$\tt{Amount = P(1 + \frac{R}{100} ) {}^{n}}$

$\tt{= P( + \frac{5}{100} ) {}^{2} = P \times (1.05 {}^{2} )}$

$\tt{= 1.1025p}$

$\tt{C.I = A - P = 1.1025P - P}$

$\tt{= 0.1025P}$

Given that,

$\tt{C.I - S.I = rs15}$

$\tt{0.1025P - 0.1P = Rs\:15228}$

$\tt{0.0025P = Rs\:15}$

$\tt{P = Rs \: 6000}$

Now,

S.I for kamal,

$\tt{0.1P = 0.1 \times 6000 = Rs \: 600}$

C.I for Anand,

$\tt{0.1025P = 0.1025 \times 6000 = Rs \: 615}$

Answer 2

Answer:

Firstly, we would find SI, for calculation of SI, we use the formula of $SI = \frac{PRT}{100}$

In the question, time was given=2 years and Rate is 5% p.a

Therefore,

$\implies SI = \frac{P \times 2 \times 5}{100}$

$\implies SI = \frac{P }{10}$

$\implies SI =0.1 P$

Now, Calculation for CI

Amount = $P ( \frac{1+r}{100}) ^{n}$

$Amount = P( 1+\frac{r}{100}) ^{n}$

$Amount = P( 1+\frac{5}{100}) ^{2}$

$Amount= 1.025 P$

$Now,$

$CI = A - P$

$CI = 1.025P - P$

$CI = 0.025 P$

$As, \: the \: question \: says \: CI - SI = Rs 15$

$0.125P - 0.1P = 15228$

$And, \: calculating \: this \: gives \: us \: P = 6000$

$Now, \: let \: us \: Calculate \: Kamal's \: and \: Anand's \: share$

$0.1P = 0.1 \times 6000 = Rs 600 (SI \: for \: kamal)$

$0.1025P=0.1025 \times 6000=Rs615 (CI \: for \:anand)$