In how many years will a certain sum becomes 5 times itself at 25% per annum under simple interest

A. 8 years

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Solution(By Examveda Team)
If the sum be P.Amount (A)=3×P=3PSimple interest (S.I)=A−P=3P−P=2PLet the sum (P) be x.Then, simple interest (S.I)=2xRate of interest (R)=25%Time =TS.I=P×R×T100⇒T=100×S.IP×R =100×2xx×25=4×2=8Hence, 8 years required.Hence, the correct option is (b).
How many years will the sum becomes 5 times itself?
How long will it take for an amount to become 5 times of itself at 20% per annum simple interest?
How many years will a certain sum becomes three times itself at 25% per annum under simple interest?
How many years will the sum of money becomes five times at 8% pa simple interest?

B. 10 years

C. 12 years

D. 14 years

Solution(By Examveda Team)

$$\eqalign{ & {\text{Let principal = P}} \cr & \therefore {\text{amount = 3P}} \cr & {\text{Interest = 3P}} - {\text{P}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = 2P}} \cr & {\text{According to the question,}} \cr & {\text{2P = }}\frac{{{\text{P}} \times {\text{R}} \times {\text{20}}}}{{100}} \cr & \Rightarrow {\text{R = 10% }} \cr} $$
Let after t years it will become double
$$\eqalign{ & {\text{Hence,}} \cr & {\text{Interest = 2P}} - {\text{P = P}} \cr & \Rightarrow {\text{P = }}\frac{{{\text{P}} \times 10 \times {\text{t}}}}{{100}} \cr & \Rightarrow {\text{t = 10 years}} \cr} $$

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CT 01: General English (Synonyms and Antonyms)

10 Questions 10 Marks 10 Mins

Given:

Amount = 9 × Principal

Rate = 25%

Formula used:

Simple Interest = (Principal × Rate × Time)/100

Simple Interest = Amount - Principal

Calculation:

Let the sum be Rs. x and the number of years be t

According to the question,

Amount = 9x

Simple Interest = Amount - Principal

⇒ Simple Interest = 9x – x = 8x

Simple Interest = (Principal × Rate × Time)/100

⇒ 8x = (x × 25 × t)/100

⇒ t = 32

∴ In 32 years, the sum becomes 9 times itself.

Last updated on Sep 26, 2022

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CT 1: International and National Awards

10 Questions 10 Marks 8 Mins

Given:

The rate of interest at which principal becomes 5 times of itself = 10%

Formula used:

S.I = (PTR)/100

A = P + S.I

where, S.I = simple interest, P = principal, T = time, R = rate of interest

Calculation:

Let the principal be P and amount be A.

According to the question,

Amount = 5 times of principal

⇒ A = 5 × P

⇒ P + S.I = 5P

⇒ S.I = 4P

Now, S.I = (PTR)/100

⇒ 4P = (P × T × 10)/100

⇒ 4 = T/10

⇒ T = 40 years

∴ The principal becomes 25 times of itself at 10% simple interest in 40 years.

Last updated on Sep 22, 2022

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