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

*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​

2 thoughts on “*The difference between simple interest and compound interest at the rate of 10% for two years on an amount is Rs. 20. Find the pr”

  1. Given :

    • Difference between simple Interest and Compound Interest = Rs. 20
    • Rate = 10%
    • Time = 2 years

    To find :

    • Principal

    Concept :

    → Formula to calculate Simple Interest :-

    [tex] \star \quad\boxed{\pmb{ \sf{Simple \: \: Interest = \dfrac{P \times R \times T}{100}}}}[/tex]

    → Formula to calculate Compound Interest :-

    [tex]\\ \star \quad \boxed{\pmb{ \sf Compound \: \: Interest = P\Bigg[1 + \dfrac{r}{100}\Bigg]^n – P}}[/tex]

    where,

    • P = Principal
    • R = Rate
    • T and n = Time

    Solution :

    Let the Sum [Principal] as P.

    Simple Interest :-

    [tex] \\ \dashrightarrow\sf \quad Simple \: \: Interest = \dfrac{P \times R \times T}{100}[/tex]

    [tex] \\ \dashrightarrow\sf \quad Simple \: \: Interest = \dfrac{P \times 10 \times 2}{100}[/tex]

    [tex] \\ \dashrightarrow\sf \quad Simple \: \: Interest = \dfrac{P \times 1 \not0 \times 2}{10 \not0}[/tex]

    [tex] \\ \dashrightarrow\sf \quad Simple \: \: Interest = \dfrac{P \times 2}{10}[/tex]

    [tex] \\ \dashrightarrow\sf \quad Simple \: \: Interest = \dfrac{2P}{10}[/tex]

    [tex] \\ \dashrightarrow\sf \quad \pmb{ \quad Simple \: \: Interest =Rs. \: \dfrac{2P}{10}}[/tex]

    Compound Interest :-

    [tex] \\ \dashrightarrow\sf \quad Compound \: \: Interest = P\Bigg[1 + \dfrac{r}{100}\Bigg]^n – P[/tex]

    [tex] \\ \dashrightarrow\sf \quad Compound \: \: Interest = P\Bigg[1 + \dfrac{10}{100}\Bigg]^2 – P[/tex]

    [tex] \\ \dashrightarrow\sf \quad Compound \: \: Interest = P\Bigg[1 + \dfrac{1 \not0}{10 \not0}\Bigg]^2 – P[/tex]

    [tex] \\ \dashrightarrow\sf \quad Compound \: \: Interest = P\Bigg[1 + \dfrac{1}{10}\Bigg]^2 – P[/tex]

    [tex] \\ \dashrightarrow\sf \quad Compound \: \: Interest = P\Bigg[\dfrac{10 + 1}{10}\Bigg]^2 – P[/tex]

    [tex] \\ \dashrightarrow\sf \quad Compound \: \: Interest = P\Bigg[\dfrac{11}{10}\Bigg]^2 – P[/tex]

    [tex] \\ \dashrightarrow\sf \quad Compound \: \: Interest = P\Bigg[\dfrac{11}{10} \times \dfrac{11}{10} \Bigg] – P[/tex]

    [tex] \\ \dashrightarrow\sf \quad Compound \: \: Interest = P\Bigg[\dfrac{121}{100} \Bigg] – P[/tex]

    [tex] \\ \dashrightarrow\sf \quad Compound \: \: Interest = \dfrac{121}{100}P – P[/tex]

    [tex] \\ \dashrightarrow\sf \quad Compound \: \: Interest = \dfrac{121P – 100P}{100}[/tex]

    [tex] \\ \dashrightarrow\sf \quad Compound \: \: Interest = \dfrac{21P}{100}[/tex]

    [tex] \\ \dashrightarrow \quad \sf \pmb{ Compound \: \: Interest = \dfrac{21P}{100}}[/tex]

    According to the question,

    ★ Compound Interest – Simple Interest= Rs. 20

    [tex] \\ \dashrightarrow\sf \quad\dfrac{21P}{100} – \dfrac{2P}{10} = 20[/tex]

    [tex] \\ \dashrightarrow\sf \quad\dfrac{21P – 20P}{100} = 20[/tex]

    [tex] \\ \dashrightarrow\sf \quad P = 20 \times 100[/tex]

    [tex] \\ \dashrightarrow\sf \quad P = 2000[/tex]

    Answer → Option (4)

    • Principal = ₹ 2000
  2. Given : Difference between Compound Interest and Simple interest is Rs.20 , The rate is 10% p.a & the time is 2 yrs

    Need To Find : The Principal.

    ⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

    ❍ Let’s Consider the Principal be P .

    ⠀⠀⠀⠀⠀Finding Simple interest :

    [tex]\dag\:\:\it{ As,\:We\:know\:that\::}\\[/tex]

    [tex]\qquad \dag\:\:\bigg\lgroup \sf{ Simple \:Interest \:: \dfrac{P\times R \times T }{100} }\bigg\rgroup \\\\[/tex]

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

    ⠀⠀⠀⠀⠀⠀[tex]\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}\\[/tex]

    [tex]\qquad \longmapsto\sf Simple \:Interest \:= \dfrac{ P \times 10 \times 2 }{100} \\ [/tex]

    [tex]\qquad \longmapsto\sf Simple \:Interest \:= \dfrac{ P \times \cancel {10} \times 2 }{10\cancel {0}} \\ [/tex]

    [tex]\qquad \longmapsto\sf Simple \:Interest \:= \dfrac{P \times 2 }{10} \\ [/tex]

    [tex]\qquad \longmapsto\sf Simple \:Interest \:= \dfrac{2P }{10} \\ [/tex]

    [tex]\qquad \longmapsto\bf \bigg( 0.2P \bigg) \qquad\: \longrightarrow\:\: Simple \:Interest \\ [/tex]

    ⠀⠀⠀⠀⠀Finding Compound interest :

    [tex]\dag\:\:\it{ As,\:We\:know\:that\::}\\[/tex]

    [tex]\qquad \dag\:\:\bigg\lgroup \sf{ Compound \:Interest \:: P \bigg( 1 +\dfrac{R }{100}\bigg) ^T – P }\bigg\rgroup \\\\[/tex]

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

    ⠀⠀⠀⠀⠀⠀[tex]\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}\\[/tex]

    [tex]\qquad \longmapsto\sf Compound \:Interest \:= P\bigg( 1 + \dfrac{ 10 }{100}\bigg)^2 – P \\ [/tex]

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

    [tex]\qquad \longmapsto\sf Compound \:Interest \:= P\bigg( 1 + \dfrac{ 1 }{10}\bigg)^2 – P \\ [/tex]

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

    [tex]\qquad \longmapsto\sf Compound \:Interest \:= P\bigg( \dfrac{ 11 }{10}\bigg)^2 – P \\ [/tex]

    [tex]\qquad \longmapsto\sf Compound \:Interest \:= P\bigg( \cancel {\dfrac{ 11 }{10}}\bigg)^2 – P \\ [/tex]

    [tex]\qquad \longmapsto\sf Compound \:Interest \:= P\bigg( 1.1\bigg)^2 \\ [/tex]

    [tex]\qquad \longmapsto\sf Compound \:Interest \:= P\bigg( 1.21\bigg) – P \\ [/tex]

    [tex]\qquad \longmapsto\sf Compound \:Interest \:= 1.21P – P \\ [/tex]

    [tex]\qquad \longmapsto\bf \bigg( Rs. \:0.21P\bigg) \qquad\: \longrightarrow\:\: Compound \:Interest \\ [/tex]

    ⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

    ⠀⠀⠀⠀⠀⠀[tex]\underline {\boldsymbol{\star\:According \: To \: Question \: \: \::}}\\[/tex]

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

    [tex]\qquad \longmapsto \sf 0.21P – 0.2P =20 \\ [/tex]

    [tex]\qquad \longmapsto \sf 0.01P =20 \\ [/tex]

    [tex]\qquad \longmapsto \sf P =\cancel {\dfrac{20}{0.01}} \\ [/tex]

    [tex]\qquad \longmapsto \frak{\underline{\purple{\:P = Rs.2,000 }} }\bigstar \\[/tex]

    Therefore,

    ⠀⠀⠀⠀⠀[tex]\therefore {\underline{ \mathrm {\:Principal \:is\:\bf{Rs.2,000}}}}\\[/tex]

    ⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

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