1. X borrows a sum of Rs.100,000 from a bank @ 10% p.a. compounded annually for 2 years. He then lends Rs.20,000, compounded every 8 months @ 10%, to each of his five friends for a period of two years. At the end of two years, X collects all the money from his friends and clears his debt with the bank. How much money did X make at the end of the two-year period ?
A. 12,100
B. 14,100
C. 15,100
D. 4,971
E. 13,200
Sol. The amount to be paid to bank after 2 years will be 100000 × (1.1)2 = Rs.121,000.
A 2-year period will be made up of three 8-month periods, each of which will cost each of the friends 10%.
The amount that each of the friends will pay back after 2 years will be 20000 × (1.1)3 = Rs.26620.
So, the total sum of money collected from the five friends will be 5 × 26620 = Rs.133,100.
After clearing his debt with the bank, X will have made 133100 – 121000 = Rs.12,100.
2. X lent Rs 2500 to Y for 4 years and Rs 4000 to Z for 3 years on simple interest at the same rate of interest and received Rs 4400 in all from both of them as interest. The rate of interest per annum is:
A. 25%
B. 17%
C. 22%
D. 20%
E. None of these
Sol. Let the rate of interes be R%. Then,
(2500*R*4)/100 + (4000*R*3)/100 = 4400
R = 4400/220 = 20%.
3. 16 men and 12 women can complete a work in 8 days, if 20 men can complete the same work in 16 days, in how many days 16 women can complete the same piece of work ?
A. 8
B. 12
C. 10
D. 15
E. 9
Sol. Lets assume it take 'w' days for 1 women to complete the job.
Then, 16/(16*20) + 12/w = 1/8
w = 160 days
Now for 16 women it will be, = 160/16 = 10 days.
4. If A's salary is 10,000 less than B's salary and B's salary is 15,000 less than C's salary and sum of their salaries is 65,000. Find the salary of A.
A. 15,000
B. 10,000
C. 12,000
D. 20,000
E. 5,000
Sol. Lets assume the salary of C be 'x'
Then, salary of B = x - 15,000
salary of A = x - 25,000
Now sum of these salaries is,
x + x - 15,000 + x - 25,000 = 65,000
Solving,
x = 35,000
A's salary = 35,000 - 25,000 = 10,000.
5. The sum of the ages of P and Q is 25 yrs more than the age of R.The present age of Q is 5 yrs more than the age of R. Find the present age of P ?
A. 15
B. 20
C. 12
D. 10
E. 16
Sol. Given, P + Q = 25 + R
Also, given, Q = 5 + R
Putting the value of Q in the 1st eqn, we get,
P + 5 + R = 25 + R
P = 20 yrs.
6. In a family, father’s age is twice that of son's age. Father is 10 years older than mother. Daughter is 20 years younger than his mother and 5 years younger than his brother. What is the age of the father?
A. 52 years
B. 50 years
C. 58 years
D. 55 years
E. None of these
Sol. Le the age of father be 'x'
Then age of son will be = x/2
Age of mother will be = (x-10)
Age of daughter will be = (x-10-20) = (x-30)
Also given,
x/2 - 5 = x - 30
x = 50 yrs.
7. After replacing an old member by a new member, it was found that the average age of five members of a club is same as it was 3 years ago. The difference between the ages of the replaced and the new members is:
A. 2 years
B. 4 years
C. 8 years
D. 15 years
E. None of these
Sol. Increase in ages of five members in 3 years = 3*5 = 15 yrs
Since the avg. age remains same, therefore required difference = 15 yrs.
8. The ratio of the present age of X to that of Y is 3 : 11. Y is 12 years younger than Z. Z’s age after 7 years will be 85 years. What is the present age of X’s mother, who is 25 years older than X ?
A. 43 years
B. 67 years
C. 45 years
D. 69 years
E. None of these
Sol. Present age of Z = 85 - 7 = 78
Present age of Y = 78 - 12 = 66
Present age of X = (3/11)*66 = 18
Present age of X's mother = 18 + 25 = 43 yrs.
9. At present, Tina is eight times her daughter’s age. 8 years from now, the ratio of the ages of Tina and her daughter will be 10 : 3. What is Tina’s present age?
A. 32 years
B. 40 years
C. 36 years
D. Cannot be determined
E. None of these
Sol. Given T = 8D
where T is the age of tina
And D is the age of daughter
Also, (8D+8)/(D+8)=10/3
Solving, we get D=4
Tina's present age = 8D = 8*4 = 32 yrs.
10. The age of the father is 30 years more than the son’s age. Ten years hence, the father’s age will become three times the son’s age that time. What is the son’s present age in years?
A. Eight
B. Seven
C. Five
D. Cannot be determined
E. None of these
Sol. Let the son's present age be x yrs.
Then the father's present age is (x+30) yrs.
Father's age after 10 yrs = (x+40) yrs
Son's age after 10 yrs = (x+10) yrs
According to the question:
(x+40)=3(x+10)
x = 5 yrs.
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