6. If I invest Rs 3000 at a simple interest for 4 years, I earn a certain amount. However, if I invest Rs 3500 at the same rate, for the same duration, I would earn Rs 130/- more. Find the rate of interest.
a. 6.5%
b. 10.50%
c. 12%
d. 13%
∴ 140R - 120R = 130
∴ R = 6.5%
7. A small broker lends his money in parts to some farmers in the village at simple interest. He lends the money as follow and earns an interest of Rs 297 at the end. Find the amount he lends.
a. 3950
b. 4200
c. 4500
d. 5500
Make denominators common. We have 5, 3 and 5 in denominators.
5 x 3 = 15
Simple interest for all parts = Rs. 297
Making denominators common.
∴ P= 4500
8. Rohit lends his 40800 Rs in two parts at simple interest. He lends one part for a period of 8 years at a rate of 6.25%. The other part he lends for 5 years at a rate of 7%. Both the parts earn him the same interest. Find the value of the smaller part of money.
a. 1300
b. 16800
c. 19200
d. 20100
∴ 50A = 35 x 40800 - 35A
∴ 85A = 35 x 40800
∴ A = 8400
Smaller amount is Rs. 16800
By direct observation we can say that 16800 is smaller - as it is smaller than half of 40800.
9. Mr. Sharma has a debt of Rs. 1078/- which he wants to completely pay off in 6 years. The rate of interest he is charged is 9% pa. Find the value of his yearly installments.
a. Rs.118.35
b. Rs.126.55
c. Rs.146.35
b. Rs.156.25
So in this case, n=6
∴ 1st installment will have interest for 5 years (n-1 = 6-1=5 years)
2nd installment will have interest for 4 years (n-2 = 6-2=4 years)
3rd installment will have interest for 3 years (n-3 = 6-3= 3 years)
4th installment will have interest for 2 years (n-4 = 6-4= 2 years)
5th installment will have interest for 1 year (n-5 = 6-5= 1 year)
6th installment will have no interest (n-6 = 6-6= 0 years)
Total Amount = 6 Installments + Interest on those 6 Installments
Now here, rate of interest is same for all installments = R = 9%
P = Rs. 100 (same amount Rs. 100 for all installments)
From above rule we can calculate effective time period 'T'
T (for interest calculation) = 5 years + 4 years + years + 2 years + 1 year + 0 years
∴ T = 15 years
For installment of Rs. 100 : Total Amount = Rs. 735
For ? installment : Total Amount is Rs. 1078
∴ 1078 x 100 = 735 x ?
10. Anuj has some extra money which he decides to lend on interest. He lends 40% of the money at a rate of 15% p.a., half of the remaining money at 10% pa and all the money left at 18% p.a. If the interest was calculated on the complete amount he lent, find the rate of interest.
a. 13.4% p.a.
b. 13.33% p.a.
c. 14.4% p.a.
d. 14.33% p.a.
a. 6.5%
b. 10.50%
c. 12%
d. 13%
Answer: a. 6.5%
Explanation:
Let Simple Interest be S
∴ S2 - S1 = Rs. 130
| Simple Interest = | PRT |
| 100 |
| ∴ | P2 x R2 x T2 | - | P1 x R1 x T1 | = 130 |
| 100 | 100 |
| ∴ | 3500 x R x 4 | - | 3000 x R x 4 | = 130 |
| 100 | 100 |
∴ 140R - 120R = 130
∴ R = 6.5%
7. A small broker lends his money in parts to some farmers in the village at simple interest. He lends the money as follow and earns an interest of Rs 297 at the end. Find the amount he lends.
| Amount | Rate of interest |
|---|---|
| 1/5 part of the amount | 3% |
| 1/3 part | 5% |
| 2/5 parts | 9% |
| Remaining amount | 11% |
a. 3950
b. 4200
c. 4500
d. 5500
Answer: c. 4500
Explanation:
Original amount = P
Consider time T = 1 year
| Parts of amounts are | 1 | , | 1 | , | 2 | and remaining amount |
| 5 | 3 | 5 |
| Remaining amount = 1 - ( | 1 | + | 1 | + | 2 | ) |
| 5 | 3 | 5 |
5 x 3 = 15
| ∴ Remaining Amount = 1- ( | 1 x 3 | + | 1 x 5 | + | 2 x 3 | ) = 1- ( | 3 | + | 5 | + | 6 | ) = 1- | 14 | = | 1 |
| 5 x 3 | 3 x 5 | 5 x 3 | 15 | 15 | 15 | 15 | 15 |
| ∴ | P/5 x 3 x 1 | + | P/3 x 5 x 1 | + | 2P/5 x 9 x 1 | + | P/15 x 11 x 1 | = 297 |
| 100 | 100 | 100 | 100 |
| ∴ | 3P | + | 5P | + | 18P | + | 11P | = 297 x 100 |
| 5 | 3 | 5 | 15 |
| ∴ | 9P | + | 25P | + | 18P | + | 11P | = 297 x 100 |
| 15 | 15 | 15 | 15 |
8. Rohit lends his 40800 Rs in two parts at simple interest. He lends one part for a period of 8 years at a rate of 6.25%. The other part he lends for 5 years at a rate of 7%. Both the parts earn him the same interest. Find the value of the smaller part of money.
a. 1300
b. 16800
c. 19200
d. 20100
Answer: b. 16800
Explanation:
Two parts are = A and (40800 - A)
Time period and Simple interest are same for both
| Simple Interest = | PRT |
| 100 |
| ∴ | A x 6.25 x 8 | = | (40800-A) x 7 x 5 |
| 100 | 100 |
∴ 85A = 35 x 40800
∴ A = 8400
Smaller amount is Rs. 16800
By direct observation we can say that 16800 is smaller - as it is smaller than half of 40800.
9. Mr. Sharma has a debt of Rs. 1078/- which he wants to completely pay off in 6 years. The rate of interest he is charged is 9% pa. Find the value of his yearly installments.
a. Rs.118.35
b. Rs.126.55
c. Rs.146.35
b. Rs.156.25
Answer: c. Rs.146.35
Explanation:
First take Installment amount = P = Rs. 100
Total installments = 6 (One installment per year)
Simple and Easy rule -
If there are 'n' installments, then, 1st installment will have interest for (n-1) years, 2nd will have interest for (n-2) years and so on.
So in this case, n=6
∴ 1st installment will have interest for 5 years (n-1 = 6-1=5 years)
2nd installment will have interest for 4 years (n-2 = 6-2=4 years)
3rd installment will have interest for 3 years (n-3 = 6-3= 3 years)
4th installment will have interest for 2 years (n-4 = 6-4= 2 years)
5th installment will have interest for 1 year (n-5 = 6-5= 1 year)
6th installment will have no interest (n-6 = 6-6= 0 years)
Total Amount = 6 Installments + Interest on those 6 Installments
| ∴ Total Amount = (6 x 100) + | P x R x T |
| 100 |
Now here, rate of interest is same for all installments = R = 9%
P = Rs. 100 (same amount Rs. 100 for all installments)
From above rule we can calculate effective time period 'T'
T (for interest calculation) = 5 years + 4 years + years + 2 years + 1 year + 0 years
∴ T = 15 years
| ∴ Total Amount = 600 + | 100 x 9 x 15 | = 600+ 135 = 735 |
| 100 |
For ? installment : Total Amount is Rs. 1078
∴ 1078 x 100 = 735 x ?
| ∴ ? = | 1078 x 100 | = Rs.146.35 |
| 735 |
10. Anuj has some extra money which he decides to lend on interest. He lends 40% of the money at a rate of 15% p.a., half of the remaining money at 10% pa and all the money left at 18% p.a. If the interest was calculated on the complete amount he lent, find the rate of interest.
a. 13.4% p.a.
b. 13.33% p.a.
c. 14.4% p.a.
d. 14.33% p.a.
Answer: c. 14.4% p.a.
