Question

*The difference between simple interest and compound interest at the rate of 10% for two years on an amount is Rs. 20. Find the principal value?*

1️⃣ ₹.100
2️⃣ ₹ 200
3️⃣ ₹. 20000
4️⃣ ₹ 2000​

Answer 1

Answer :

4️⃣ ₹2,000

Explanation :

The difference between simple interest and compound interest at the rate of 10% for 2 tear is ₹20.

Find the principal.

Let's take the principal as ‘p’

We know that,

→ S. I. = p × r × t/100

→ S. I. = p × 10 × 2/100

→ S. I. = 20p/100

And also,

The C. I. = Amount - principal

Or,

→ p(1 + r/100)ⁿ - p

→ p(1 + 10/100)² - p

→ p(11/10)² - p

→ 121p/100 - p

→ 21p/100

Given,

→ C. I. - S. I. = 20

→ 21p/100 - 20p/100 = 20

→ p/100 = 20

→ p = 2000

∴ The principal is ₹2,000

_____________________

Formula used :

1. Amount = p(1 + r/100)ⁿ

• p = principal
• r = rate
• n = time

2. Simple interest = p × r × t/100

Answer 2

$\bf{Given\::}\begin{cases} \sf { Difference \:between \:Compound \:Interest \:and\:Simple \:Interest \:is\::Rs.20}\\ \sf { Rate \:is\:10\:\% }\\ \sf {Time\:is\:2yrs\:}\end{cases}$

Need To Find : The Principal. ⠀⠀⠀

⠀⠀━━━━━━━━━━━━━━━━━━━

⠀ Let's Consider the Principal be P .

⠀⠀⠀⠀⠀Finding Simple interest :

$\dag\:\:\it{ As,\:We\:know\:that\::}$

$\qquad \dag\:\:\bigg\lgroup \sf{ Simple \:Interest \:: \dfrac{P\times R \times T }{100} }\bigg\rgroup$

⠀⠀⠀⠀⠀Here P is the Principal , R is the Rate of Interest & T is the Time.

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad \longmapsto\sf Simple \:Interest \:= \dfrac{ P \times 10 \times 2 }{100}$

$\qquad \longmapsto\sf Simple \:Interest \:= \dfrac{ P \times \cancel {10} \times 2 }{10\cancel {0}}$

$\qquad \longmapsto\sf Simple \:Interest \:= \dfrac{P \times 2 }{10}$

$\qquad \longmapsto\sf Simple \:Interest \:= \dfrac{2P }{10}$

$\qquad \longmapsto\bf \bigg( 0.2P \bigg) \qquad\: \longrightarrow\:\: Simple \:Interest$

⠀⠀⠀⠀⠀Finding Compound interest :

$\dag\:\:\it{ As,\:We\:know\:that\::}$

$\qquad \dag\:\:\bigg\lgroup \sf{ Compound \:Interest \:: P \bigg( 1 +\dfrac{R }{100}\bigg) ^T - P }\bigg\rgroup$ ⠀

⠀⠀⠀⠀Here P is the Principal , R is the Rate of Interest & T is the Time.

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad \longmapsto\sf Compound \:Interest \:= P\bigg( 1 + \dfrac{ 10 }{100}\bigg)^2 - P$

$\qquad \longmapsto\sf Compound \:Interest \:= P\bigg( 1 + \dfrac{ \cancel{10} }{10\cancel{0}}\bigg)^2 -P$

$\qquad \longmapsto\sf Compound \:Interest \:= P\bigg( 1 + \dfrac{ 1 }{10}\bigg)^2 - P$

$\qquad \longmapsto\sf Compound \:Interest \:= P\bigg( \dfrac{ 10 +1 }{10}\bigg)^2- P$

$\qquad \longmapsto\sf Compound \:Interest \:= P\bigg( \dfrac{ 11 }{10}\bigg)^2 - P$

$\qquad \longmapsto\sf Compound \:Interest \:= P\bigg( \cancel {\dfrac{ 11 }{10}}\bigg)^2 - P$

$\qquad \longmapsto\sf Compound \:Interest \:= P\bigg( 1.1\bigg)^2$

$\qquad \longmapsto\sf Compound \:Interest \:= P\bigg( 1.21\bigg) - P$

$\qquad \longmapsto\sf Compound \:Interest \:= 1.21P - P$

$\qquad \longmapsto\bf \bigg( Rs. \:0.21P\bigg) \qquad\: \longrightarrow\:\: Compound \:Interest$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀ ⠀⠀⠀⠀

⠀⠀$\underline {\boldsymbol{\star\:According \: To \: Question \: \: \::}}$

• Difference between Compound Interest and Simple interest is Rs.20 .

$\qquad \longmapsto \sf 0.21P - 0.2P =20$

$\qquad \longmapsto \sf 0.01P =20$

$\qquad \longmapsto \sf P =\cancel {\dfrac{20}{0.01}}$

$\qquad \longmapsto \frak{\underline{\purple{\:P = Rs.2,000 }} }\bigstar$

Therefore, ⠀⠀⠀⠀⠀

$\therefore {\underline{ \mathrm {\:Principal \:is\:\bf{Rs.2,000}}}}$ ⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀