Simple interest
- The simple interest on a sum of money is 4/9 of the principal and the number of years is equal to the rate percent per annum. The rate per annum is :
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We know that
SI = Principal × Time × Rate 100
According to question,SI = 4 P 9
& R = T (numerically)∴ 4 P = P × R × R 9 100 ∴ R2 = 400 9
∴ R2 = √(400 / 9)
Correct Option: B
We know that
SI = Principal × Time × Rate 100
According to question,SI = 4 P 9
& R = T (numerically)∴ 4 P = P × R × R 9 100 ∴ R2 = 400 9
∴ R2 = √(400 / 9)R = 20 = 6 2 % 3 3
- The difference between the simple interest received from two different sources on ₹1500 for 3 years is 13.50. The difference between their rates of interest is:
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Let r1, and r2 be the required rate of interest Then,
As per the given in question ,13.50 = 1500 × 3 × r1 - 1500 × 3 × r2 100 100 = 4500 (r1 - r2) 100 r1 - r2 = 135 = 27 450 90 r1 - r2 = 3 = 0.3% 10
Second method to solve this question :
P1 = Rs. 1500, R1, T1 = 3 years.
P2 = Rs. 1500, R2, T2 = 3 years.
S.I. = Rs. 13.5013.50 = 1500 × R2 × 3 - 1500 × R1 × 3 100 1350 = 4500(R2 - R1) 100 100
Correct Option: C
Let r1, and r2 be the required rate of interest Then,
As per the given in question ,13.50 = 1500 × 3 × r1 - 1500 × 3 × r2 100 100 = 4500 (r1 - r2) 100 r1 - r2 = 135 = 27 450 90 r1 - r2 = 3 = 0.3% 10
Second method to solve this question :
P1 = Rs. 1500, R1, T1 = 3 years.
P2 = Rs. 1500, R2, T2 = 3 years.
S.I. = Rs. 13.5013.50 = 1500 × R2 × 3 - 1500 × R1 × 3 100 1350 = 4500(R2 - R1) 100 100 (R2 - R1) = 1350 = 27 4500 90 R2 - R1 = 3 = 0.3% 10
- The simple interest on a certain sum at 5% per annum for 3 years and 4 years differ by 42. The sum is :
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According to question,
Interest of one year = ₹42
Rate = 5% and Time = 1 year∴ Principal = Interest × 100 Rate × Time = 42 × 100 5 × 1
Second method to solve this question :
P1 = P, R1 = 5%,
T1 = 3years. P2 = P,
R2 = 5%, T2 = 4 years.
Difference in SI = 42
Correct Option: A
According to question,
Interest of one year = ₹42
Rate = 5% and Time = 1 year∴ Principal = Interest × 100 Rate × Time = 42 × 100 5 × 1
Second method to solve this question :
P1 = P, R1 = 5%,
T1 = 3years. P2 = P,
R2 = 5%, T2 = 4 years.
Difference in SI = 4242 = 20P - 15P 100
P = 42 × 20
P= ₹840
- The present worth of a bill due 7 months hence is ₹1200 and if the bill were
The rate percent isdue at the end of 2 1 years its present worth would be 1016. 2
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As we know that ,
SI = Principal × Time × Rate 100
Amount = Principal + SI
∴ Amount (A) = 1200 + 1200 × 7 × r 12 × 100
⇒ 1200 + 7r = A .........(i)and, 1016 + 1016 × 5 × r = A 2 × 100
Correct Option: B
As we know that ,
SI = Principal × Time × Rate 100
Amount = Principal + SI
∴ Amount (A) = 1200 + 1200 × 7 × r 12 × 100
⇒ 1200 + 7r = A .........(i)and, 1016 + 1016 × 5 × r = A 2 × 100
∴ 1016 + 25.4r = A ........(ii)
From eq. (i) and (ii) , we get
∴ 1016 + 25.4r = 1200 + 7r
⇒ 25.4r – 7r = 1200 – 1016
⇒ 18.4r = 184
⇒ r = 184 ÷ 18.4 = 10% per annum
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On a certain sum, the simple interest at the end of 6 1 years becomes 4 3 of the sum. The rate of interest is 8
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According to question ,
Simple Interest = 3 Principal 8 ∴ Rate = S.I × 100 Principal × Time Rate = 3 × 100 8 (25 / 4) Rate = 3 × 400 8 25
Rate = 6% per annum
Second method to solve this question :Here, n = 3 , T = 25 Years. 8 4 R = n × 100 T
Correct Option: B
According to question ,
Simple Interest = 3 Principal 8 ∴ Rate = S.I × 100 Principal × Time Rate = 3 × 100 8 (25 / 4) Rate = 3 × 400 8 25
Rate = 6% per annum
Second method to solve this question :Here, n = 3 , T = 25 Years. 8 4 R = n × 100 T R = 3 × 100 8 ( 25 / 4 )
R = 6%
