Question

Q.6 Simple interest on a certain sum is 16/25 of the sum. If the rate percent and the time are numerically equal, the rate percent is ____% per annum and the time is _____ years.​

Answer 1

${\large{\boxed{\underline{\mathrm{\bf{\orange{Given:-}}}}}}}$

• Simple Interest  = ${\mathsf{\dfrac{16}{25} \ of \ the \ sum}}$
• Time = Rate (numerically)

${\large{\boxed{\underline{\mathrm{\bf{\red{To \ Find:-}}}}}}}$

• Time
• Rate of Interest

${\large{\boxed{\underline{\mathrm{\bf{\pink{Formula \ Used:-}}}}}}}$

${\pink{\bigstar}} \ {\boxed{\tt{\green{S.I. = \dfrac{P \times R \times T}{100}}}}} \ {\pink{\bigstar}}$

where,

• S.I. = Simple Interest
• P = Principal
• R = Rate
• T = Time

${\large{\boxed{\underline{\mathrm{\bf{\blue{Solution:-}}}}}}}$

Let, the Principal be x,

Then, Simple Interest is ${\bf{\dfrac{16x}{25}}}$.

Let, Time and Rate of Interest be y,

According to the question by using the formula of Simple Interest, we get the following equation,

$\longmapsto {\mathsf{\dfrac{16x}{25} = \dfrac{x \times y \times y}{100}}}$

$\longmapsto {\mathsf{\dfrac{16x}{25} = \dfrac{xy^2}{100}}}$

$\longmapsto {\mathsf{\dfrac{16}{25} = \dfrac{xy^2}{100} \times \dfrac{1}{x}}}$

$\longmapsto {\mathsf{\dfrac{16}{25} = \dfrac{y^2}{100}}}$

$\longmapsto {\mathsf{16 \times 100 = 25 \times y^2}}$

$\longmapsto {\mathsf{1600 = 25y^2}}$

$\longmapsto {\mathsf{\dfrac{1600}{25} = y^2}}$

$\longmapsto {\mathsf{64 = y^2}}$

$\longmapsto {\mathsf{ \sqrt 64 = y}}$

$\longmapsto {\boxed{\mathsf{\bf{\blue{y = 8}}}}}$

${\orange{\bigstar}} \ \therefore {\boxed{\underline{\mathsf{\green{Time}{\pink{ \ is \ }{\blue{\bf{8 \ years}}}}}}}} \ {\orange{\bigstar}} \ {\mathsf{and}} \ \\ {\orange{\bigstar}} \ {\boxed{\underline{\mathsf{\green{Rate \ of \ Interest}{\pink{ \ is \ }{\blue{\bf{8 \% \ per \ annum}}}}}}}} \ {\orange{\bigstar}}$

${\huge{\green{\checkmark}}}$ ${\large{\boxed{\underline{\mathrm{\bf{\orange{Verification:-}}}}}}}$ ${\huge{\green{\checkmark}}}$

According to the question by using the formula of Simple Interest, we get the following equation,

$\longmapsto {\mathsf{\dfrac{16x}{25} = \dfrac{x \times 8 \times 8}{100}}}$

$\longmapsto {\mathsf{\dfrac{16x}{25} = \dfrac{64x}{100}}}$

$\longmapsto {\mathsf{\dfrac{16x}{25} = \dfrac{16x}{25}}}$

$\Longrightarrow {\bf{LHS=RHS}} \Longleftarrow$

${\mathsf{Hence, Verified \ \checkmark }}$

Answer 2

Answer:

Check attachment ❄️

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