1. A sum of money compounded annually becomes Rs.625 in two years and Rs.675 in three years. The rate of interest per annum is
(a) 7% (b) 8% (c) 6% (d) 5%
Direction for Question 2 : The question is followed by two statements. As the answer, Mark (a) if the question can be answered with the help of statement I alone, Mark (b) if the question can be answered with the help of statement II, alone, Mark (c) if both, statement I and statement II are needed to answer the question, and Mark (d) if the question cannot be answered even with the help of both the statements.
2. Little Beau Peep lost her sheep. She couldn’t remember how many were there. She knew she would have 400 more next year, than the number of sheep she had last year. How many sheep were there?
I. The number of sheep last year was 20% more than the year before that and this simple rate of increase continues to be the same for the next 10 years.
II. The increase is compounded annually.
3. A man invests Rs.3,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum?
(a) Rs.1,200 (b) Rs.1,300 (c) Rs.1,500 (d) Rs.2,000
4. An amount borrowed at simple interest gets tripled in 24 years. How many years does it take to get doubled, if the interest rate is same. (TITA)
5. Gopal borrows Rs. X from Ankit at 8% annual interest. He then adds Rs. Y of his own money and lends Rs. X + Y to Ishan at 10% annual interest. At the end of the year, after returning Ankit’s dues, the net interest retained by Gopal is the same as that accrued to Ankit. On the other hand, had Gopal lent Rs. X + 2Y to Ishan at 10%, then the net interest retained by him would have increased by Rs. 150. If all interests are compounded annually, then find the value of X + Y. (TITA)
Solutions
- B 2. C 3. C 4. 12 5. 4000
1.(b)For a difference of 1 year, CI can be computed as SI. Hence, from the 2nd year to the 3rd year interest earned = (675 – 650)= Rs.50 on Rs 625.
Hence, the Rate of interest 50/625 × 100 = 8% p.a.
2.(c) The statement I suggests that the number of sheep had increased by 20% last year over the previous year. But it does not suggest whether the rate of increase is annual or not.
E.g. 20% increase in a year can also be obtained by 9.5% increase over 6 months. i.e. 1.095 x 1.095 = 1.20.
The statement II however suggests that the increase is compounded annually. Hence, now we can find the answer.
If the number of sheep last year was x, then x + 400 = x(1.2)2
Hence, x = 909. Thus, we require both statements to answer the question.
3.(C) Let the amount invested at 8% be Rs x.
Then, 3000 
+ x
= (3000 + x) 
0.02x = 30 
x = 1,500
4. (12) For the amount to get tripled, the increase is 200% of the principal. If it happens in 24 years then it will take 12 years for the increase to be 100% of the principal.
5. (4000) Let X = Rs. 100a and Y = Rs. 100b
Gopal owes Ankit an interest of Rs. 8a at the end of the year and similarly Ishan owes Gopal an interest of Rs. (10a + 10b) at the end of the year.
Given that, 2 × 8a = 10a + 10b
a : b = 5 : 3 or a = 5k and b = 3k
Also, an additional amount equal to Y or 300k at 10% interest would fetch Gopal Rs. 150 more.
30k = Rs. 150 Hence, X + Y = 800k = Rs. 4000.
