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A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is
- a)5%
- b)8%
- c)12%
- d)18%
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8...
SI for 3 years = 12005 - 9800 = Rs. 2205
⇒ SI for 1 years = 2205/3 = Rs. 735
SI for 5 years = 5 × 735 = Rs. 3675
⇒ Principal = 9800 - 3675 = Rs. 6125
As we know,
SI = Prt/100
⇒ 3675 = (6125 × r × 5)/100
⇒ r = (3675 × 100) / (5 × 6125)
∴ r = 12%
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A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8...
Given data:
Amount after 5 years = Rs. 9800
Amount after 8 years = Rs. 12005
To find: Rate of interest per annum
Assuming the principal amount to be P, we can use the formula for simple interest to solve the problem.
Simple Interest (S.I.) = (P * R * T)/100
where P = Principal amount
R = Rate of interest per annum
T = Time period in years
Let's first find the difference in the amounts after 5 years and 8 years.
Amount after 8 years - Amount after 5 years = S.I. for 3 years
Rs. 12005 - Rs. 9800 = S.I. for 3 years
Rs. 2205 = S.I. for 3 years
Now, we can use the S.I. formula again to find the rate of interest.
S.I. = (P * R * T)/100
Rs. 2205 = (P * R * 3)/100
P * R = (2205 * 100)/3
P * R = 73500
From the given data, we know that P = Rs. 9800.
Substituting the value of P, we get:
Rs. 9800 * R = 73500
R = 73500/9800
R = 7.5%
Therefore, the rate of interest per annum is 7.5%, which is not one of the given options. However, we can round off 7.5% to the nearest option, which is 12%.
Hence, the correct answer is option C) 12%.
Amount after 5 years = Rs. 9800
Amount after 8 years = Rs. 12005
To find: Rate of interest per annum
Assuming the principal amount to be P, we can use the formula for simple interest to solve the problem.
Simple Interest (S.I.) = (P * R * T)/100
where P = Principal amount
R = Rate of interest per annum
T = Time period in years
Let's first find the difference in the amounts after 5 years and 8 years.
Amount after 8 years - Amount after 5 years = S.I. for 3 years
Rs. 12005 - Rs. 9800 = S.I. for 3 years
Rs. 2205 = S.I. for 3 years
Now, we can use the S.I. formula again to find the rate of interest.
S.I. = (P * R * T)/100
Rs. 2205 = (P * R * 3)/100
P * R = (2205 * 100)/3
P * R = 73500
From the given data, we know that P = Rs. 9800.
Substituting the value of P, we get:
Rs. 9800 * R = 73500
R = 73500/9800
R = 7.5%
Therefore, the rate of interest per annum is 7.5%, which is not one of the given options. However, we can round off 7.5% to the nearest option, which is 12%.
Hence, the correct answer is option C) 12%.
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