Question

The difference between the compound interest and the simple interest on a certain sum for 2 years at 6% p.a is ₹90. Find the sum.​

Answer 1

Answer- ₹ 25000
Explanation

Answer 2

Required Solution :

★ Sum = Rs 25000 ★

Given:

• The difference between the compound interest and the simple interest on a certain sum for 2 years at 6% p.a is ₹90.

To calculate:

• The sum i.e principal.

Calculation:

Here, we'll first calculate the simple interest and then compound interest as per the the given information. Then by forming the suitable equation , we'll find the sum.

→ Let the sum be "P".

Simple Interest:

$\bf { \longrightarrow S.I= \dfrac{P \times R \times T}{100} }$

Where,

• P = Principal
• R = Rate = 6 % p.a
• Time = 2 years

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$\bf { \longrightarrow S.I= \dfrac{P \times 6 \times 2}{100} }$

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$\bf { \longrightarrow S.I= \dfrac{P \times 12}{100} }$

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$\bf { \longrightarrow S.I= \dfrac{P \times 6}{50} }$

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$\bf { \longrightarrow S.I= \dfrac{P \times 3}{25} }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\bf \purple { \longrightarrow S.I= \dfrac{3P}{25} }$

Also,

Compound Interest:

$\bf { \longrightarrow C.I = Amount - Principal}$

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$\bf { \longrightarrow C.I = {P \Bigg ( 1 + \dfrac{R}{100} \Bigg )}^{n} - P}$

Where,

• P = Principal
• R = Rate = 6 % p.a
• n (number of years) = 2 years

$\bf { \longrightarrow C.I = {P \Bigg ( 1 + \dfrac{6}{100} \Bigg )}^{2}- P }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\bf { \longrightarrow C.I = {P \Bigg ( \dfrac{100 + 6}{100} \Bigg )}^{2}- P }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\bf { \longrightarrow C.I = {P \Bigg ( \dfrac{106}{100} \Bigg )}^{2}- P }$

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$\bf { \longrightarrow C.I = P \Bigg ( \dfrac{106}{100} \times \dfrac{106}{100} \Bigg )} - P$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\bf { \longrightarrow C.I = P \Bigg ( \dfrac{53}{50} \times \dfrac{53}{50} \Bigg ) - P}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\bf { \longrightarrow C.I = P \Bigg ( \dfrac{53 \times 53}{50 \times 50} \Bigg ) - P}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\bf { \longrightarrow C.I = P \times \dfrac{2809}{2500} - P }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\bf { \longrightarrow C.I =\dfrac{2809P}{2500} -P }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\bf { \longrightarrow C.I =\dfrac{2809P - 2500P}{2500} }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\bf\purple { \longrightarrow C.I =\dfrac{309P}{2500} }$

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Now, we got the value of S.I and C.I. Also, the question states that difference between C.I and S.I is ₹ 90. So,

$\bf { \longrightarrow C.I - S.I = Rs \: 90 }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\bf { \longrightarrow \dfrac{309P}{2500} - \dfrac{3P}{25} = Rs \: 90 }$

⠀⠀⠀⠀⠀⠀

$\bf { \longrightarrow \dfrac{309P - 300P}{2500} = Rs \: 90 }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\bf { \longrightarrow \dfrac{9P}{2500} = Rs \: 90 }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\bf { \longrightarrow 9P = Rs \: 90 \times 2500 }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\bf { \longrightarrow 9P = Rs \: 22500 }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\bf { \longrightarrow P = Rs \: \dfrac{22500}{9} }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\bf \orange{ \longrightarrow P = Rs \: 25000 }$

Hence, the sum is Rs 25000.

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