Simple interest
- The simple interest on a sum of money is 1/9 of the principal and the number of years is equal to rate per cent per annum. The rate per annum is
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As per the given in question , we have
Simple interest = 1 Principal 9
If the annual rate of interest be r%, thenRate = S. I × 100 Principal × Time ⇒ r = 1 × 100 9 r ⇒ r2 = 100 9
⇒ r = √100 / 9⇒ r = 10 3 ⇒ r = 3 1 % 3
Second method to solve this question :Here, n = 1 , R = T 9
RT = n × 100R2 = 1 × 100 9 R2 = 100 9
R = √100 / 9
Correct Option: C
As per the given in question , we have
Simple interest = 1 Principal 9
If the annual rate of interest be r%, thenRate = S. I × 100 Principal × Time ⇒ r = 1 × 100 9 r ⇒ r2 = 100 9
⇒ r = √100 / 9⇒ r = 10 3 ⇒ r = 3 1 % 3
Second method to solve this question :Here, n = 1 , R = T 9
RT = n × 100R2 = 1 × 100 9 R2 = 100 9
R = √100 / 9R = 10 3 R = 3 1 % 3
- If ₹12,000 is divided into two parts such that the simple interest on the first part for 3 years at 12% per annum is equal to the simple interest on the
second part for 4 1 years at 16% per annum, the greater part is 2
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Let the larger part of the sum be p
∴ Smaller part = (12000 – p)
According to the question,p × 3 × 12 = (1200 0- p) × 9 × 16 100 2 × 100
⇒ 36 p = (12000 – p ) 72
⇒ p = (12000 – p ) × 2
⇒ p + 2p = 24000
Correct Option: A
Let the larger part of the sum be p
∴ Smaller part = (12000 – p)
According to the question,p × 3 × 12 = (12000 - p) × 9 × 16 100 2 × 100
⇒ 36 p = (12000 – p ) 72
⇒ p = (12000 – p ) × 2
⇒ p + 2p = 24000
⇒ 3p = 24000⇒ p = 24000 = ₹ 8000 3
- Simple interest on 500 for 4 years at 6.25% per annum is equal to the simple interest on 400 at 5% per annum for a certain period of time. The period of time is
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Let the period of time be T years. Then,
400 × 5 × T = 500 × 6.25 × 4 100 100 T = 500 × 6.25 × 4 = 25 400 × 5 4
Correct Option: C
Let the period of time be T years. Then,
According to question ,400 × 5 × T = 500 × 6.25 × 4 100 100 T = 500 × 6.25 × 4 = 25 400 × 5 4 T = 6 1 Years. 4
- If the simple interest for 6 years be equal to 30% of the principal, it will be equal to the principal after
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Let the principal be P and rate of interest be r %
According to the question,30P = P × 6 × R 100 100
⇒ 30 = 6 R
⇒ R = 5
Now, let interest be equal to principal in T years.∴ P = P × T × 5 100 ⇒ T = 100 = 20 Years. 5
Second method to solve this question :Here , n = 30 = 3 , T = 6 Years. 100 10
⇒ RT = n × 100R × 6 = 3 × 100 10
R = 5%
As, S.I. = P
Correct Option: A
Let the principal be P and rate of interest be r %
According to the question,30P = P × 6 × R 100 100
⇒ 30 = 6 R
⇒ R = 5
Now, let interest be equal to principal in T years.∴ P = P × T × 5 100 ⇒ T = 100 = 20 Years. 5
Second method to solve this question :Here , n = 30 = 3 , T = 6 Years. 100 10
⇒ RT = n × 100R × 6 = 3 × 100 10
R = 5%
As, S.I. = P⇒ SI = P × T × R 100
100 = RT
100 = 5 × T
This is possible only when T = 20.
- A sum of ₹1500 is lent out in two parts in such a way that the simple interest on one part at 10% per annum for 5 years is equal to that on another part at 12.5% per annum for 4 years. The sum lent out at 12.5% is :
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Let the sum lent out at 12.5% be p.
∴ Sum lent out at 10% = 1500 – pNow, (1500 - p) × 10 × 5 = p × 12.5 × 4 100 100 100
⇒ 50 (1500 – p ) = 50p
⇒ 2p = 1500
Correct Option: C
Let the sum lent out at 12.5% be p.
∴ Sum lent out at 10% = 1500 – pNow, (1500 - p) × 10 × 5 = p × 12.5 × 4 100 100 100
⇒ 50 (1500 – p ) = 50p
⇒ 2p = 1500⇒ p = 1500 = ₹ 750 2
