1. A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined them after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed amount A, B and C
A. 3:7:5
B. 6:10:5
C. 6:10:7
D. 6:7:5
Answer: Option (B)
Explanation:
Let initial investment of A is 3x and B is 5x, then C investment is also 5x, but most important to note in this question is the time duration of the investment
Like, A invested for 12 months, B invested for 12 months and C invested for 6 months.
A:B:C =(3x*12):(5x*12):(5x*6)
= 36:60:30
= 6:10:5
2. A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest?
A. 3%
B. 4%
C. 5%
D. 6%
E. None of these
Answer: Option (D)
Explanation:
S.I. = Rs. (15500 - 12500) = Rs. 3000.
Rate = [latex]\frac{100 \times 3000}{12500 \times 4}[/latex] % = 6%
3. The captain of a cricket team of 11 members is 26 years old and the wicketkeeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
A. 23 years
B. 24 years
C. 25 years
D. None of these
Answer: Option (A)
Explanation:
Let the average age of the whole team by x years.
11x - (26 + 29) = 9(x -1)
11x - 9x = 46
2x = 46
x = 23.
So, average age of the team is 23 years.
4. A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
A. 8 hours
B. 10 hours
C. 12 hours
D. 24 hours
Answer: Option (C)
Explanation:
A's 1 hour's work = [latex]\frac {1}{4}[/latex];
(B + C)'s 1 hour's work =[latex]\frac {1}{3}[/latex];
(A + C)'s 1 hour's work =[latex]\frac {1}{2}[/latex].
(A + B + C)'s 1 hour's work = ([latex]\frac {1}{4}[/latex]+[latex]\frac {1}{3}[/latex])= [latex]\frac {7}{12}[/latex].
B's 1 hour's work = ([latex]\frac {7}{12}[/latex]-[latex]\frac {1}{2}[/latex])=[latex]\frac {1}{12}[/latex].
Therefore B alone will take 12 hours to do the work.
5. Convert the binary number 1001.0010 to decimal.
A. 125
B. 12.5
C. 90.125
D. 9.125
Answer: Option (D)
6. A man buys oranges at Rs 5 a dozen and an equal number at Rs 4 a dozen. He sells them at Rs 5.50 a dozen and makes a profit of Rs 50. How many oranges does he buy?
A. 30 dozens
B. 40 dozens
C. 50 dozens
D. 60 dozens
Answer: Option (C)
Explanation:
Cost Price of 2 dozen oranges Rs. (5 + 4) = Rs. 9.
Sell price of 2 dozen oranges = Rs. 11.
If profit is Rs 2, oranges bought = 2 dozen.
If profit is Rs. 50, oranges bought = (2/2) * 50 dozens = 50 dozens.
7. 64309 - 8703 + 798 - 437 = ?
A. 55606
B. 55697
C. 55967
D. 73373
E. None of these
Answer: Option (C)
Explanation:
64309 - 8703 + 798 - 437 => 65107 - 9140 = 55967.
8. When I have married 10 years ago my wife is the 6th member of the family. Today my father died and a baby born to me. The average age of my family during my marriage is the same as today. What is the age of Father when he died?
A. 50 yrs
B. 60 yrs
C. 70 yrs
D. 65 yrs
Answer: Option (B)
Explanation:
Let the Father be x years when he died
Average Age 10 years ago be A
Total Age 10 years ago = 6*A
Total Age after 10 years(Just before father's Death) = 6A + 6*10 = 6A + 60
Father Died and Baby was born => the Total number of people in the family is Same (6)
Baby born today so age of baby = 0
(6A +60 - x)/6 = 6A/6
=> A + 10 -(x/6) = A
=> x/6 = 10
=> x = 60
Therefore we can conclude that the father was 60 years old when he died.
9. The ratio between the speeds of two trains is 7: 8. If the second train runs 400 km in 4 hours, then the speed of the first train is:
A. 70 km/hr
B. 75 km/hr
C. 84 km/hr
D. 87.5 km/hr
Answer: Option (D)
Explanation:
Let the speed of two trains be 7x and 8x km/hr.
Then, 8x = 400/4 = 100
x = 100/8 = 12.5
Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr.
10. If the price has fallen by 10% what percent of its consumption be: increased so that the expenditure may be the same as before?
A. 11%
B. 10%
C. 11 1/9 %
D. 9 1/11 %
Answer: Option (C)
Explanation:
100 – 10 = 90
90------10
100------? => 11 1/9%