## Simple interest

#### Simple interest

1. An old article is available for ₹ 12,000 at cash payment or is available for ₹ 7,000 cash payment and a monthly instalment of ₹630 for 8 months. The rate per cent per annum is

1. As per the given in question , we have
Simple Interest = (7000 + 630 × 8) – 12000
Simple Interest = (7000 + 5040) – 12000
Simple Interest = 12040 – 12000 = 40
Total Principal = 5000 + 4370 + 3740 + 3110 + 2480 + 1850 + 1220 + 590 = ₹ 22360

##### Correct Option: A

As per the given in question , we have
Simple Interest = (7000 + 630 × 8) – 12000
Simple Interest = (7000 + 5040) – 12000
Simple Interest = 12040 – 12000 = 40
Total Principal = 5000 + 4370 + 3740 + 3110 + 2480 + 1850 + 1220 + 590 = ₹ 22360

 Rate = 40 × 100 ×12 ≈ 2.1% 22360 × 1

1. 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 ?

1. 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

1. 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 ?

1. Case I,
Here , Principal = ₹ 800 , Amount = ₹ 920
S.I. = Amount - Principal = 920 – 800 = ₹ 120

 Rate = 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 = ₹ 120

 Rate = Interest × 100 Principal × Time

 = 120 × 100 = 5% per annum 800 × 3

Case II,
Rate = 8% per annum
 S.I. = 800 × 8 × 3 = ₹ 192 800 × 3

∴ Amount = Principal + S.I. = (800 + 192) = ₹ 992

1. A sum of ₹ 10,000 is lent partly at 8% and remaining at 10% per annum. If the yearly interest on the average is 9.2%, the two parts are :

1. Let p be lent at 8%, then (10000 – p) is lent at 10%.
According to question ,

 ∴ 10000 × 9.2 × t = p × 8 × t + (10000 - p) × 10 × t 100 100 100

 ⇒ 920000 = 8pt + (10000 - p)10t 100 100 100

##### Correct Option: A

Let p be lent at 8%, then (10000 – p) is lent at 10%.
According to question ,

 ∴ 10000 × 9.2 × t = p × 8 × t + (10000 - p) × 10 × t 100 100 100

 ⇒ 920000 = 8pt + (10000 - p)10t 100 100 100

⇒ 92000t = 8pt + (10000 – p) 10t
⇒ 92000t = 8pt + (10000 – p) 10t
⇒ 92000 = 8p + 100000 – 10p
⇒ 2p = 8000
⇒ p = 4000
∴ First part = ₹ 4000
Second part = 10000 - 4000 = ₹ 6000

1. A sum of money was lent at simple interest at a certain rate for 3 years. Had it been lent at 2.5% per annum higher rate, it would have fetched ₹540 more. The money lent was :

1. If the sum lent be Rs. p, then

 p × 2.5 × 3 = 540 100

 p = 540 × 100 = ₹ 7200 2.5 × 3

Second method to solve this question :
P1 = P, R1 = R, T1 = 3
P2 = P, R2 = R + 2.5% , T2 = 3 , S.I. = Rs. 540
 ∴ SI = P2 × R2 × T2 - P1 × R1 × T1 100

##### Correct Option: D

If the sum lent be Rs. p, then

 p × 2.5 × 3 = 540 100

 p = 540 × 100 = ₹ 7200 2.5 × 3

Second method to solve this question :
P1 = P, R1 = R, T1 = 3
P2 = P, R2 = R + 2.5% , T2 = 3 , S.I. = Rs. 540
 ∴ SI = P2 × R2 × T2 - P1 × R1 × T1 100

 540 = P × (R + 2.5%) × 3 - P × R × 3 100

54000 = 7.5P
 P = 540000 75

P = ₹ 7200