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A certain sum becomes 5 times in 3 years, at simple interest, then in how many years it will become 13 times?
- a)6
- b)13
- c)9
- d)12
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A certain sum becomes 5 times in 3 years, at simple interest, then in ...
Let, amount = P and rate = r%
In first case,
Time = 3 years
Amount = 5P
According to problem,
⇒ (P × r × 3)/100 = 5P – P
⇒ 3Pr/100 = 4P
⇒ r = 400/3
In second case,
Rate = (400/3) %
Let, time = n years
Amount = 13P
According to problem,
⇒ [P × (400/3) × n]/100 = 13P – P
⇒ 4Pn/3 = 12P
⇒ 4n/3 = 12
⇒ n = 12 × ¾
⇒ n = 9
∴ In 9 years it will become 13 times.
In first case,
Time = 3 years
Amount = 5P
According to problem,
⇒ (P × r × 3)/100 = 5P – P
⇒ 3Pr/100 = 4P
⇒ r = 400/3
In second case,
Rate = (400/3) %
Let, time = n years
Amount = 13P
According to problem,
⇒ [P × (400/3) × n]/100 = 13P – P
⇒ 4Pn/3 = 12P
⇒ 4n/3 = 12
⇒ n = 12 × ¾
⇒ n = 9
∴ In 9 years it will become 13 times.
Most Upvoted Answer
A certain sum becomes 5 times in 3 years, at simple interest, then in ...
To solve this question, we need to use the formula for simple interest:
Simple Interest = (Principal * Rate * Time) / 100
Let's assume the principal amount is P.
Given that the principal amount becomes 5 times in 3 years, we can write the equation as:
5P = P + (P * R * 3) / 100
Simplifying this equation, we get:
5P = P + 3PR/100
Multiplying both sides by 100 to eliminate the fraction, we have:
500P = 100P + 3PR
Simplifying further, we get:
400P = 3PR
Dividing both sides by P and R, we have:
400 = 3R
R = 400/3
Now, we need to find the time it will take for the principal amount to become 13 times.
Let's assume the time required is T.
Using the same formula for simple interest, we can write the equation as:
13P = P + (P * R * T) / 100
Simplifying this equation, we get:
13P = P + (P * (400/3) * T) / 100
Multiplying both sides by 100 to eliminate the fraction, we have:
1300P = 100P + (400PT) / 3
Simplifying further, we get:
1200P = (400PT) / 3
Dividing both sides by P and 400T/3, we have:
1200 = 400T/3
Multiplying both sides by 3/400, we get:
T = (1200 * 3) / 400
T = 9
Therefore, it will take 9 years for the principal amount to become 13 times. Hence, option C is the correct answer.
Simple Interest = (Principal * Rate * Time) / 100
Let's assume the principal amount is P.
Given that the principal amount becomes 5 times in 3 years, we can write the equation as:
5P = P + (P * R * 3) / 100
Simplifying this equation, we get:
5P = P + 3PR/100
Multiplying both sides by 100 to eliminate the fraction, we have:
500P = 100P + 3PR
Simplifying further, we get:
400P = 3PR
Dividing both sides by P and R, we have:
400 = 3R
R = 400/3
Now, we need to find the time it will take for the principal amount to become 13 times.
Let's assume the time required is T.
Using the same formula for simple interest, we can write the equation as:
13P = P + (P * R * T) / 100
Simplifying this equation, we get:
13P = P + (P * (400/3) * T) / 100
Multiplying both sides by 100 to eliminate the fraction, we have:
1300P = 100P + (400PT) / 3
Simplifying further, we get:
1200P = (400PT) / 3
Dividing both sides by P and 400T/3, we have:
1200 = 400T/3
Multiplying both sides by 3/400, we get:
T = (1200 * 3) / 400
T = 9
Therefore, it will take 9 years for the principal amount to become 13 times. Hence, option C is the correct answer.
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A certain sum becomes 5 times in 3 years, at simple interest, then in how many years it will become 13 times?a)6b)13c)9d)12Correct answer is option 'C'. Can you explain this answer?
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