Type 2: Problems On Simple Interest (SI) When Rates are different for different years
Question 1. Nisha borrowed some money at the rate of 5% p.a. for the first two years. She again borrowed at the rate of 10% p.a. for the next three years. Later at the rate of 15% p.a. for the rest of the years. Total interest paid by her was Rs. 15000 at the end of 10 years. Calculate the amount of money she borrowed?
Options:
A. Rs. 15005
B. Rs. 20000
C. Rs. 15000
D. Rs. 10000
Solution: According to the question,
r1 = 5% , T1 = 2 years
r2 = 10% , T2 = 3 years
r3 = 15% , T3 = 5 years
(since, beyond 5 years rate is 14%)
Simple interest = 15000
Therefore, P = \frac{15000 * 100}{5*2 +10*3 +15*4 }
=\frac{1500000}{10 + 30 + 60 }
= \frac{1500000}{100}
= Rs. 15000
Correct option: C
Question 2. Rahul invests some amount of money in three different schemes for 5 years, 10 years and 15 years at 10%, 12% and 15% Simple Interest respectively. At the completion of each scheme, he gets the same interest. Find out the ratio of his investment?
Options:
A. 3: 9: 15
B. 10: 24: 45
C. 10: 24: 40
D. 9: 24: 45
Solution: If a certain sum of money is lent out in n parts in such a manner that equal sum of money is obtained at simple interest on each part where interest rates are 10 %, 12 %,15% respectively and time periods are 5 years , 10 years , 15 years respectively.
Let the three amounts be Rs. x, Rs. y and Rs. z,
Then , According to question
\frac{x × 10 × 5}{100} = \frac{y× 12 × 10}{100} = \frac{z × 15 × 15}{100}
50 x = 120 y = 225 z = k(say)
10 x = 24 y = 45 z = k
\frac{k}{10}: \frac{k}{24}: \frac{k}{45}
Hence, the ratio of his investment will be
\frac{k}{10}: \frac{k}{24}: \frac{k}{45}
10 : 24 : 45
Correct option: B
Question 3. Ram tool a loan for Rs.10000 from bank for a period of 3 years. The bank charged the interest rates as 5% for first year, 7% for second year and 9% for the third year. Find the amount he has to pay back to the bank after three years?
Options:
A. Rs. 18500
B. Rs. 145000
C. Rs. 15100
D. Rs 12100.
Solution: Simple Interest = 5% + 7% + 9% = 21%.
Amount = Principal + Rate of Interest.
Principal is 100% of the amount.
Therefore, Amount = 100% + 21%.= 121%
According to the question, total amount to be paid
A =\frac{121 * 10000}{100}
A = 12100
Therefore, the amount that Ram has to pay back to the bank after three years Rs 12100.
Correct option: D
IN Type 2 Question 2 Answer should be 20:15:8
please check