Question

simple interest on a certain sum is 16/25 of the sum. find the rate and time if both are numerically equal {HINT = ( T=R) P = x S.I = 16/25 x)
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Answer 1

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▪ Simple Interest on a certain sum is 16/25 of the sum. Find the rate and time of both are numerically equal.

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▪ Simple Interest on a certain sum is 16/25 of the sum...

• let the sum be Rs. x

• simple interest = Rs. (16/25)x

it's given in the question that.....

Rate and Time are numerically equal

so , let us assume...

• Rate (R) = a % p.a.

• Time ( T ) = a years

☆ Simple Interest ( S. I. )

${ \boxed{ \bold{ \red{ \: \: S.I. = \frac{P \times R \times T }{100} \: \: }}}}$

where,

¤ P = Principal

¤ R = Rate

¤ T = Time

substituting the above assumed values in the formula.....

${ \bold{ S .I. = \frac{P \times R \times T }{100} }}$

${ \bold{ \implies{ \frac{16}{25} x = \frac{x \times a \times a}{100}}}}$

${ \bold{ \implies{ \frac{16}{25} = \frac{ {a}^{2} }{100} }}}$

${ \bold{ \implies{ {a}^{2} = \frac{16 \times 100}{25} }}}$

${ \bold{ \implies{a = \sqrt{16 \times 4}}}}$

${ \boxed{ \bold{ \red{ \: a = 8 \: }}}}$

therefore,

☆ Rate = 8% p.a.

☆ Time = 8 years

Answer 2

Answer:

Time =8 years

Rate  =8%

Step-by-step explanation:

Simple Interest on a certain sum is 16/25 of the sum

let the sum be Rs. x

Simple interest = Rs. (16/25)x

it's given in the question that

Rate and Time are numerically equal

so , let us assume...

Rate (R) = a % p.a.

Time ( T ) = a years

SI=P*T*R/100

16/25x=x*a*a/100

16/25=a^2/100

a^2=16

a=8

Time =a =8 years

Rate =a =8%

Hope u like my answer :)

therefore,

☆ Rate = 8% p.a.

☆ Time = 8 years