1. A contractor undertook to do a certain piece of work in 9 days. He employed certain number of men, but 6 of them, being absent from the very first day, the rest could finish the work in 15 days. The number of men originally employed was:
a) 12
b) 15
c) 18
d) 24
2. If 6 years are subtracted from the present age of Gagan and the reminder is divided by 18, then the present age of his grandson Anup is obtained. If Anup is 2 years younger to Madan whose age is 5 years, then what is Gagan's present age?
a) 48 years
b) 60 years
c) 84 years
d) 96 years
3. To win an election, a candidate needs 3/4 of the votes cast. If after 2/3 of the votes have been counted, a candidate has 5/6 of what he needs, then what part of the remaining vote does he still need?
a) 1/8
b) 3/8
c) 1/10
d) 1/4
4. The difference between compound interest and simple interest on a sum for 2 years at 10% per annum, when the interest is compounded annually is Rs 16. If the interest were compounded half-yearly, the difference in two interests would be:
a) Rs 24.81
b) Rs 26.90
c) Rs 31.61
d) Rs 32.40
5. If a commission of 10% is given on written price of an article, the gain is 20%. If the commission is increased to 20%, the gain is:
a) 6 2/3%
b) 7 1/4%
c) 12 1/2%
d) 13 1/3%
6. A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and completely passes them in 9 and 10 seconds respectively. Find the length of the train.
a) 45m
b) 50m
c) 54m
d) 72m
7. In a business, A and C invested amounts in the ratio 2:1, whereas the ratio between amounts invested by A and B was 3:2. If Rs. 1,57,300 was their profit, how much amount did B receive?
a) Rs 24,200
b) Rs 36,300
c) Rs 48,400
d) Rs 72,600
8. A motorboat whose speed is 15 kmph in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream ( in kmph) is :
a) 4
b) 5
c) 6
d) 10
9. The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings so as to increase his average runs by 4?
a) 2
b) 4
c) 70
d) 76
10. In what ratio must a grocer mix two varieties of pulses costing Rs 15 and Rs 20 per Kg respectively so as to get a mixture worth Rs 16.50 per Kg?
a) 3 : 7
b) 5 : 7
c) 7 : 3
d) 7 : 5
Answers
1.(b)
Let there be x men at the beginning
Less men, More days
15 : 9 : : x : (x -6)
15(x - 6) = 9x
6x = 90
x = 15
2.(b)
Anup's age = (5 - 2) = 3 years
Let Gagan's age be x years.
Then, ( x -6)/18 = 3
x - 6 = 54
x = 60
3.(b)
Let the number of votes cast be x
Then number of votes required = 3x/4
Counted votes = 2x/3. Uncounted votes = ( x - 2x/3) = x/3
Votes won by the candidate = 5/6 of 3x/4 = 5x/8
Remaining votes required = (3x/4 - 5x/8) = x/8
Required fraction = (x/8)/(x/3) = 3/8
4(a)
For first year, S.I = C.I
Now, Rs 16 is the S.I for 1 year
Rs 10 is S.I on Rs 100
Rs 16 is SI on Rs (100/10 x 16) = Rs 160
So, SI on principal for 1 year at 10% is Rs 160
Principal = Rs(100 x 160)/(10 x 1) = Rs 1600
Amount for 2 years compounded half yearly = Rs(1600 x ( 1+ 5/100)^4) = Rs 1944.81
C.I = Rs(1944.81 - 1600) = Rs 344.81
S.I = Rs(1600 x 10 x 2)/100 = 320
Hence difference = 24.81
5.(a)
Let Marked Price be Rs 100.
Then SP = Rs (90/100 x 100) = Rs 90. Gain = 20%
CP = Rs(100/120 x 90) = Rs 75
New commission = Rs 20; New SP = Rs 80
New profit = (5/75 x 100)% = 6 2/3%
6.(b)
2 kmph = (2 x 5/18) m/sec = 5/9 m/sec
4 kmph = 10/9 m/sec
Let the length of the train be x meters and its speed be y m/sec
Then, x/(y - 5/9) = 9 and x/(y - 10/9) = 10
9y - 5 = x and 10(9y - 10) = 9x
On solving we get: x = 50
Hence length = 50m
7.(c)
A : B = 3 : 2 and A : C = 2 : 1
A : B : C = 6 : 4: 3
B's share = (4/13 x 157300) = Rs 48,400
8.(b)
Let the speed of the stream be x kmph
Speed downstream = (15 + x) kmph, Speed upstream = (15 - x) kmph
30/(15 + x) + 30/(15 - x) = 4 1/2
900/(225 - x^2) = 9/2
9x^2 = 225
x^2 = 25
x = 5
9.(d)
Average after 11 innings = 36
Required number of runs = (36 x 11) - (32 x 10)
= 396 - 320 = 76//
10.(c)
CP of 1st Kind---------------CP of 2nd Kind
Rs 15...................................Rs. 20
......................16.50.......................
3.50..........................................1.50
Required rate = 3.50 : 1.50 = 7 : 3
1.(b)
Let there be x men at the beginning
Less men, More days
15 : 9 : : x : (x -6)
15(x - 6) = 9x
6x = 90
x = 15
2.(b)
Anup's age = (5 - 2) = 3 years
Let Gagan's age be x years.
Then, ( x -6)/18 = 3
x - 6 = 54
x = 60
3.(b)
Let the number of votes cast be x
Then number of votes required = 3x/4
Counted votes = 2x/3. Uncounted votes = ( x - 2x/3) = x/3
Votes won by the candidate = 5/6 of 3x/4 = 5x/8
Remaining votes required = (3x/4 - 5x/8) = x/8
Required fraction = (x/8)/(x/3) = 3/8
4(a)
For first year, S.I = C.I
Now, Rs 16 is the S.I for 1 year
Rs 10 is S.I on Rs 100
Rs 16 is SI on Rs (100/10 x 16) = Rs 160
So, SI on principal for 1 year at 10% is Rs 160
Principal = Rs(100 x 160)/(10 x 1) = Rs 1600
Amount for 2 years compounded half yearly = Rs(1600 x ( 1+ 5/100)^4) = Rs 1944.81
C.I = Rs(1944.81 - 1600) = Rs 344.81
S.I = Rs(1600 x 10 x 2)/100 = 320
Hence difference = 24.81
5.(a)
Let Marked Price be Rs 100.
Then SP = Rs (90/100 x 100) = Rs 90. Gain = 20%
CP = Rs(100/120 x 90) = Rs 75
New commission = Rs 20; New SP = Rs 80
New profit = (5/75 x 100)% = 6 2/3%
6.(b)
2 kmph = (2 x 5/18) m/sec = 5/9 m/sec
4 kmph = 10/9 m/sec
Let the length of the train be x meters and its speed be y m/sec
Then, x/(y - 5/9) = 9 and x/(y - 10/9) = 10
9y - 5 = x and 10(9y - 10) = 9x
On solving we get: x = 50
Hence length = 50m
7.(c)
A : B = 3 : 2 and A : C = 2 : 1
A : B : C = 6 : 4: 3
B's share = (4/13 x 157300) = Rs 48,400
8.(b)
Let the speed of the stream be x kmph
Speed downstream = (15 + x) kmph, Speed upstream = (15 - x) kmph
30/(15 + x) + 30/(15 - x) = 4 1/2
900/(225 - x^2) = 9/2
9x^2 = 225
x^2 = 25
x = 5
9.(d)
Average after 11 innings = 36
Required number of runs = (36 x 11) - (32 x 10)
= 396 - 320 = 76//
10.(c)
CP of 1st Kind---------------CP of 2nd Kind
Rs 15...................................Rs. 20
......................16.50.......................
3.50..........................................1.50
Required rate = 3.50 : 1.50 = 7 : 3
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