Question

Illustration 3 :
Simple interest on a certain sum for 4 years at 7% p.a. is more than simple
interest on the same sum for 2.5 years at the same rate by 840. Find the
principal amount.​

Answer 1

Answer:

• The principal amount is Rs 8000.

Step-by-step explanation:

Given that:

• Simple interest on a certain sum for 4 years at 7% p.a. is more than simple interest on the same sum for 2.5 years at the same rate by 840.

To Find:

• The principal amount.

Let us assume:

• The principal amount be P.

Formula used:

• S.I. = (P × R × T)/100

Where,

• S.I. = Simple interest
• P = Principal amount
• R = Rate of interest
• T = Time

Finding the principal amount:

According to the question.

⟶ (P × 7 × 4)/100 = (P × 7 × 2.5)/100 + 840

⟶ 28P/100 = 17.5P/100 + 840

⟶ 0.28P = 0.175P + 840

⟶ 0.28P - 0.175P = 840

⟶ 0.105P = 840

⟶ P = 840/0.105

⟶ P = 8000

∴ Principal amount = Rs 8000

Answer 2

Given : Simple interest on a certain sum for 4 years at 7% p.a. is more than simple interest on the same sum for 2.5 years at the same rate by 840.

Exigency To Find : The Principal amount.

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

❍ Let's Consider the Principal amount be P .

$\dag\:\:\sf{ As,\:We\:know\:that\::}\\\\ \qquad\maltese\:\:\bf \:Formula\:for\:Simple\:Interest\:\::$

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

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

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\: According \:to\: the \:Question \::}}$

⠀⠀⠀⠀⠀━━━ Simple interest on a certain sum for 4 years at 7% p.a. is more than simple interest on the same sum for 2.5 years at the same rate by 840.

$\qquad:\implies \sf 1^{st} \: Simple \:Interest \: = \: 2^{nd} \: Simple \:Interest\:\:+ 840$

$\qquad:\implies \sf \dfrac{ P \times 7 \:\times 4 }{100} = \dfrac{ P \times 7 \:\times 2.5 }{100} + 840$

$\qquad:\implies \sf \dfrac{ P \times 28 }{100} = \dfrac{ P \times 17.5 }{100} + 840$

$\qquad:\implies \sf \dfrac{ 28P }{100} = \dfrac{ 17.5P }{100} + 840$

$\qquad:\implies \sf \cancel {\dfrac{ 28P }{100}} = \dfrac{ 17.5P }{100} + 840$

$\qquad:\implies \sf 0.28 \:P = \dfrac{ 17.5P }{100} + 840$

$\qquad:\implies \sf 0.28 \:P = \cancel {\dfrac{ 17.5P }{100}} + 840$

$\qquad:\implies \sf 0.28 \:P = 0.175P + 840$

$\qquad:\implies \sf 0.28 \:P- 0.175 P = 840$

$\qquad:\implies \sf 0.105 P = 840$

$\qquad:\implies \sf P = \dfrac{840}{0.015}$

$\qquad:\implies \sf P = \cancel {\dfrac{840}{0.015}}$

$\qquad:\implies \bf P = 8000$

$\qquad:\implies \frak{\underline{\purple{\:P = Rs.8000 }} }\:\:\bigstar$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:Principal \:amount\:\:is\:\bf{Rs.8000}}}}$

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