Question

In what time will a sum amount of 5 times of itself at the rate of 7.5% per annum.​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Time=\frac{160}{3}\:years}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Rate\%(r) = 7.5\% \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Time \: after \: which \: amount \: is \: 5 \: times \: of \: principal = ?$

• According to given question :

$\tt \circ \: Let \: principal \: be \: x \\ \\ \tt \circ \: Amount = 5x \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies A= p +S.I \\ \\ \tt: \implies 5x = x + S.I\\ \\ \tt: \implies S.I= 4x \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies S.I= \frac{p \times r \times t}{100} \\ \\ \tt: \implies 4x = \frac{x \times 7.5 \times t}{100} \\ \\ \tt: \implies \frac{4x \times 100}{x \times 7.5} = t \\ \\ \tt: \implies t = \frac{400}{7.5} \\ \\ \tt: \implies t = \frac{16}{0.3} \\ \\ \green{\tt: \implies t = \frac{160}{3} \: years}$

Answer 2

GIVEN :-

Rate(r) = 7.5 %

TO FIND :-

The time(t) when the amount will be equal to 5 times of the principal.

SOLUTION :-

Let the principal be P. Then the amount will be 5P.

We know,

S.I = Amount - Principal

⇒S.I = 5P - P

⇒S.I = 4P

We also know,

S.I = (p × r × t)/100

Putting the known values :-

⇒ 4P = (P × 7.5 × t)/100

⇒ 400P = 7.5 Pt

⇒ t = 400P/7.5P

⇒ t = 4000/75

⇒ t = 160/3 years

∴ Therefore, the sum will be five times of the principal in 160/3 years.