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An amount becomes 4 times in 10 years when kept in a scheme of simple interest. In how many years will it become 7 times?
- a)16
- b)20
- c)24
- d)28
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
An amount becomes 4 times in 10 years when kept in a scheme of simple ...
GIVEN:
Time = 10 years
Amount = 4 × Principal
Time = 10 years
Amount = 4 × Principal
FORMULA USED:
SI = P × R × T / 100
SI = P × R × T / 100
CALCULATION:
Let, principal = p
Time = 10 years
Rate of interest = r%
According to problem,
⇒ 4p - p = p × r × 10/100
⇒ r = 30
Let, in x years it will become 7 times.
Principal = p
Rate = 30%
Time = x years
According to problem,
⇒ 7p - p = p × 30 × x/100
⇒ x = 20
∴ In 20 years principal will become 7 times.
Let, principal = p
Time = 10 years
Rate of interest = r%
According to problem,
⇒ 4p - p = p × r × 10/100
⇒ r = 30
Let, in x years it will become 7 times.
Principal = p
Rate = 30%
Time = x years
According to problem,
⇒ 7p - p = p × 30 × x/100
⇒ x = 20
∴ In 20 years principal will become 7 times.
Most Upvoted Answer
An amount becomes 4 times in 10 years when kept in a scheme of simple ...
Given:
- Amount becomes 4 times in 10 years.
- Scheme of simple interest is used.
To find:
In how many years will the amount become 7 times?
Solution:
Let's assume the principal amount as P.
Step 1: Find the rate of interest (R)
The formula for calculating the amount using simple interest is:
A = P + P * R * T
where A is the final amount, P is the principal amount, R is the rate of interest, and T is the time in years.
In this case, the amount becomes 4 times the principal in 10 years. So we can write the equation as:
4P = P + P * R * 10
Simplifying the equation:
4P = P(1 + 10R)
4 = 1 + 10R
10R = 3
R = 3/10
R = 0.3 or 30%
Therefore, the rate of interest is 30%.
Step 2: Find the time (T)
Now, we need to find the time it takes for the amount to become 7 times the principal.
Using the same formula with the new variables:
7P = P + P * 0.3 * T
Simplifying the equation:
7 = 1 + 0.3T
6 = 0.3T
T = 6/0.3
T = 20
Therefore, it will take 20 years for the amount to become 7 times the principal.
Answer:
In 20 years, the amount will become 7 times the principal. Therefore, the correct option is (b) 20.
- Amount becomes 4 times in 10 years.
- Scheme of simple interest is used.
To find:
In how many years will the amount become 7 times?
Solution:
Let's assume the principal amount as P.
Step 1: Find the rate of interest (R)
The formula for calculating the amount using simple interest is:
A = P + P * R * T
where A is the final amount, P is the principal amount, R is the rate of interest, and T is the time in years.
In this case, the amount becomes 4 times the principal in 10 years. So we can write the equation as:
4P = P + P * R * 10
Simplifying the equation:
4P = P(1 + 10R)
4 = 1 + 10R
10R = 3
R = 3/10
R = 0.3 or 30%
Therefore, the rate of interest is 30%.
Step 2: Find the time (T)
Now, we need to find the time it takes for the amount to become 7 times the principal.
Using the same formula with the new variables:
7P = P + P * 0.3 * T
Simplifying the equation:
7 = 1 + 0.3T
6 = 0.3T
T = 6/0.3
T = 20
Therefore, it will take 20 years for the amount to become 7 times the principal.
Answer:
In 20 years, the amount will become 7 times the principal. Therefore, the correct option is (b) 20.
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An amount becomes 4 times in 10 years when kept in a scheme of simple interest. In how many years will it become 7 times?a)16b)20c)24d)28Correct answer is option 'B'. Can you explain this answer?
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