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Sum / Principal

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Question 135

The simple interest on a certain sum for 2.5 yr at 12 % per annum is ₹ 300 less than the simple interest on the same sum for 4.5 yr at 8 % per annum. Find the sum.

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Solution

Let the sum be x.
Given that,
$P_{1} = x, R_{1} = 12 % a n d T_{1} = 2.5 y r = \frac{5}{2} y r$
and
$P_{2} = x, R_{2} = 8 % a n d T_{2} = 4.5 y r = \frac{9}{2} y r$

According to the question,
$I_{2} - I_{1} = 300 \Rightarrow \frac{P_{2} \times R_{2} \times T_{2}}{100} - \frac{P_{1} \times R_{1} \times T_{1}}{100} = 300 \Rightarrow \frac{x \times 8 \times 9}{2 \times 100} - \frac{x \times 12 \times 5}{2 \times 100} = 300 \Rightarrow 72 x - 60 x = 300 \times 200 \Rightarrow 12 x = 60000$
$x$ = ₹ 5000
Hence, the sum or the principal is ₹ 5000.

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Sum / Principal

Standard VII Mathematics

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Question 135 The simple interest on a certain sum for 2.5 yr at 12 % per annum is ₹ 300 less than the simple interest on the same sum for 4.5 yr at 8 % per annum. Find the sum.

Let the sum be x. Given that, P1=x,R1=12% and T1=2.5 yr=52yr and P2=x,R2=8% andT2=4.5 yr=92yr According to the question, I2−I1=300⇒P2×R2×T2100−P1×R1×T1100=300⇒x×8×92×100−x×12×52×100=300⇒72x−60x=300×200⇒12x=60000 x = ₹ 5000 Hence, the sum or the principal is ₹ 5000.

Question 135

The simple interest on a certain sum for 2.5 yr at 12 % per annum is ₹ 300 less than the simple interest on the same sum for 4.5 yr at 8 % per annum. Find the sum.