Simple interest
 A sum of Rs. 800 amounts to Rs. 920 in 3 years at the simple interest rate. If the rate is increased by 3% p.a., what will be the sum amount to in the same period ?

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Case I,
Here , Principal = ₹ 800 , Amount = ₹ 920
S.I. = Amount  Principal = 920 – 800 = ₹ 120Rate = Interest × 100 Principal × Time = 120 × 100 = 5% per annum 800 × 3
Case II,
Rate = 8% per annum
Correct Option: A
Case I,
Here , Principal = ₹ 800 , Amount = ₹ 920
S.I. = Amount  Principal = 920 – 800 = ₹ 120Rate = Interest × 100 Principal × Time = 120 × 100 = 5% per annum 800 × 3
Case II,
Rate = 8% per annumS.I. = 800 × 8 × 3 = ₹ 192 800 × 3
∴ Amount = Principal + S.I. = (800 + 192) = ₹ 992
 A person who pays income tax at the rate of 4 paise per rupee, find that a fall of interest rate from 4% to 3.75% diminishes his net yearly income by ₹48. What is his capital ?

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If the capital after tax deduction be p, then
p × (4 – 3.75) % = 48⇒ p × 0.25 = 48 100 ⇒ p × 25 = 48 10000 ⇒ p = 48 400
⇒ p = 48 × 400 = ₹ 19200
Correct Option: C
If the capital after tax deduction be p, then
p × (4 – 3.75) % = 48⇒ p × 0.25 = 48 100 ⇒ p × 25 = 48 10000 ⇒ p = 48 400
⇒ p = 48 × 400 = ₹ 19200∴ Required capital = 19200 × 100 = ₹ 20000 96
 A and B borrowed Rs. 3000 and Rs. 3200 respectively at the same rate of
rate of interest.interest for 2 1 years. If B paid Rs. 40 more interest than A, find the 2

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Rate of interest = r % per annum
SI = Principal × Time × Rate 100
According to the question,3200 × 5 × r  3000 × 5 × r = 40 100 × 2 200
⇒ 80r – 75r = 40
⇒ 5r = 40 ⇒ r = 40 ÷ 5 = 8% per annum
Second method to solve this question :Here, P_{1} = Rs. 3000, R_{1} = R, T_{1} = 5 years 2
Correct Option: C
Rate of interest = r % per annum
SI = Principal × Time × Rate 100
According to the question,3200 × 5 × r  3000 × 5 × r = 40 100 × 2 200
⇒ 80r – 75r = 40
⇒ 5r = 40 ⇒ r = 40 ÷ 5 = 8% per annum
Second method to solve this question :Here, P_{1} = Rs. 3000, R_{1} = R, T_{1} = 5 years 2 P_{2} = Rs. 3200, R_{2} = R, T_{2} = 5 years 2
Difference S.I. = Rs. 40⇒ 40 = 3200 × R × (5 / 2)  3000 × R × (5 / 2) 100
⇒ 4000 = 8000R – 7500R
⇒ R = 8%
 The rate of simple interest for which a sum of money becomes 5 times of itself in 8 years is :

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Let Principal = Rs. p
According to question ,
∴ Amount = Rs. 5p
Simple Interest = Amount  Principal = Rs. (5p – p) = Rs. 4p∴ Rate = SI × 100 Principal × Time
Correct Option: C
Let Principal = Rs. p
According to question ,
∴ Amount = Rs. 5p
Simple Interest = Amount  Principal = Rs. (5p – p) = Rs. 4p∴ Rate = SI × 100 Principal × Time Rate = 4p × 100 = 50% per annum p × 8
 In what time will the simple interest be 2/5 of the principal at 8 percent per annum?

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Let the principal be p.
∴ Simple Interest = 2 p 5
Rate = 8% per annum∴ Time = Interest × 100 Principal × Rate Time = (2 / 5)p × 100 = 40 = 5 years p × 8 8
Second method to solve this question :Here, n = 2 and R = 8% 5
⇒ RT = (n × 100)T = n × 100 R
Correct Option: C
Let the principal be p.
∴ Simple Interest = 2 p 5
Rate = 8% per annum∴ Time = Interest × 100 Principal × Rate Time = (2 / 5)p × 100 = 40 = 5 years p × 8 8
Second method to solve this question :Here, n = 2 and R = 8% 5
⇒ RT = (n × 100)T = n × 100 R T = 2 × 100 5 8
T = 5 years