Directions(1-5) : Find the missing numbers in the given series
1. 2, 24, _, 320, 750, 1512
A. 45
B. 54
C. 81
D. 27
E. None of these
Sol. E) None of these.
1³×2 = 2
2³×3 = 24
3³×4 = 108
4³×5 = 320
5³×6 = 750
6³×7 = 1512
2. 2, 7, 17.5, 35.5, _, 102
A. 55.5
B. 63
C. 60.5
D. 50.5
E. None of these
Sol. 2.5*2 + 2 = 7
3.5*3 + 7 = 17.5
4.5*4 + 17.5 = 35.5
5.5*5 + 35.5 = 63
6.5*6 + 63 = 102.
3. 5, 17, 72, _, 2204, 15438
A. 360
B. 350
C. 321
D. 318
E. None of these
Sol. 5*3 + 2 = 17
17*4 + 4 = 72
72*5 + 6 = 366
366*6 + 8 = 2204
4. 12, 20, _, 57, -68
A. 2
B. 15
C. -7
D. -2
E. None of these
Sol. 12 + 2^3 = 20
20 - 3^3 = -7
-7 + 4^3 = 57
57 - 5^3 = -68
5. 68, 62, _, 54, 84
A. 76
B. 72
C. 74
D. 70
E. None of these
Sol. 68 - (2*3) = 62
62 + (3*4) = 74
74 - (4*5) = 54
54 + (5*6) = 84
6. The average of 11 numbers is 12. The average of first 6 is 11 and that of last 6 is 12, what is the middle number ?
A. 8
B. 6
C. 7
D. 5
E. None of these
Sol. Sum of 11 numbers = 11×12 = 132.
Sum of first 6 numbers = 11×6 = 66.
Sum of last numbers = 12×6 = 72.
Thus the middle number is = (72+66) - 132 = 6.
7. A train is travelling at a speed of 40 kmph. A man is going in the same direction parallel to the train at speed of 25 kmph. If the train crosses the man in 48 seconds, the length of the train is ?
A. 100m
B. 150m
C. 200m
D. 250m
E. None of these
Sol. Relative speed = 40 - 25 = 15 kmph
Length of the train = 15×(48/3600)×1000× = 200m.
8. A rectangular carpet has an area of 100 sq.m and a perimeter of 54 m. The length of its diagonal is ?
A. 23
B. 27
C. 24
D. 25
E. None of these
Sol. Perimeter of a rectangle = 2(l+b)
2(l+b) = 54
l+b = 27
Area of rectangle = l×b
l×b = 100
Diagonal = √l²+b² = √(l+b)² - 2lb = √(27)² - 2×100 = √529 = 23.
9. An amount of Rs 2109 is distributed among A, B and C in the ratio 3:7:9. B's share is more than C's share by ?
A. Rs 444
B. Rs 379
C. Rs 265
D. Rs 215
E. None of these
Sol. Let the shares of A, B & C be 3X, 7X and 9X respectively.
3X + 7X + 9X = 2109
19X = 2109
X = 111.
Difference in the share of B & C = 7X - 3X = 4X = 4×111 = Rs 444.
10. A man rows upstream 17 km and 29 km downstream, taking 5 hours each time. The velocity of the current is ?
A. 1
B. 1.2
C. 1.4
D. 1.6
E. None of these
Sol. Let speed of boat be 'x' kmph
And speed of current be 'y' kmph
According to the question,
x - y = 17/5
and
x + y = 29/5
Solving, we get, y = 1.2 mph.
11. Prachi sold two steel chairs for Rs 500 each. On one he gains 25% and on other, he loses 20%. How much does she gain or lose in th whole transaction ?
A. 1.5% gain
B. 2% gain
C. 2.4% loss
D. 2% loss
E. None of these
Sol. S.P. of 1st chair = Rs 500
Gain = 25%
Thus, C.P. of 1st chair will be = (500×100)/(100+25) = 400
S.P. of 2nd chair = Rs 500
Loss = 20%
C.P. of 2nd chair = (500×100)/(100-20) = 625.
Total SP = Rs 1000
Total CP = Rs 1025
loss% = (25/1025)×100 = 2.43%.
12. 3 men can do apiece of work in 18 days. 6 boys can also do the same work in 18 days.In how many days, 4 men and 4 boys together will finish the same work ?
A. 12
B. 6
C. 10
D. 8
E. None of these
Sol. According to the question,
3 men = 6 boys
thus, 1 man = 2 boys
4 men + 4 boys = 4 men + 2 men = 6 men
3 men can do work in 18 days
thus, 1 man can do work in 18×3 days
6 men can do the work in (18×3)/6 = 9 days.
13. Six years ago, karan was twice as old as sushma. If the ratio of their present ages is 9:5 respectively, what is the difference between their present ages in years ?
A. 24
B. 30
C. 5
D. 1
E. Cant be determined
Sol. Let the present ages of karan and sushma be x and y..
According to the question,
x/y = 9/5
and
(x-6) = 2(y-6)
Solving, we get, x = 54 & y = 30
Thus, difference = 54-30 = 24 years.
14. An item sold at 10% discount gives 17% profit, what would be the percentage profit if discount increased to 15% ?
A. 12%
B. 11%
C. 10%
D. 10.5%
E. None of these
Sol. Lets assume C.P. to be 100
Then S.P. will be 117 (as profit 17%)
Now, 117 = (90/100)*M.P. (As discount is 10%)
M.P.= 130
When discount 15%, S.P. = (85/100)*130 = 110.5
Thus, profit % = 10.5 %.
15. What is the area of the square whose side is equal to the side of an equilateral triangle with area 9√3?
A. 16
B. 36
C. 18
D. 24
E. None of these
Sol. Lets say the side of the square = side of the equilateral triangle be 'a'.
Now, area of the triangle is given 9×√3,thus,
[a×a×√3]/4 = 9×√3
a = 6.
16. 15 women can complete 10% of the work in 7 days, 25 women worked for 31.5 days then what fraction of the work is remaining ?
A. 1/5
B. 1/6
C. 1/4
D. 1/3
E. None of these
Sol. 25 women complete the work in = (15×70)/25 = 42 days
25 women per day work = 1/42
25 women 31.5 day work = 31.5/42
Remaining work = (1 - 31.5/42) = 1/4.
17. There are 32 cards in a bag numbered from 1 to 32. 2 cards are drawn one by one without replacement. Find the probability that both are even numbered cards.
A. 1/16
B. 15/62
C. 16/62
D. 15/31
E. None of these
Sol. Required Probability = (16/32)×(15/31) = 15/62.
18. A and B enetered into a partnership with the investments of 25500 and 15000. At the end of 1 year B invested 9000 rs more. The total profit earned at the end of 2 yrs is 45,000 then find the difference between the shares of A and B.
A. 5000 RS
B. 6000 RS
C. 7000 RS
D. 8000 RS
E. None of these
Sol. (25500×2):(15000 + 24000)
= 17:13
Required Difference = (4/30)*45000 = Rs 6000.
19. Two trains of length 200m each running in the same direction cross each other in 80 sec. If the speed of faster traiin is 72 km/hr, then find the speed of the slower train.
A. 36 km/hr
B. 45 km/hr
C. 54 km/hr
D. 57 km/hr
E. None of these
Sol. Relative speed = 400/9 = 5m/s
Speed of faster train = 72×(5/18) = 20m/s
Speed of slower train = 20 - 5 = 15m/s
or 15×(18/5) = 54 km/h.
20. Out of three numbers, the first is twice the second and is half of the third. If the avg. of 3 numbers is 56, the three numbers in order are:
A. 48,96,24
B. 48,24,96
C. 96,24,48
D. 96,48,24
E. None of these
Sol. Sum of three numbers = 56×3 = 168
Let 2nd no. = x
1st no. = 2x
3rd no. = 4x
x + 2x + 4x = 168
The no.s are 48,24,96.
The following line graph gives the ratio of the amounts of imports by a company to the amount of exports from that company over the period from 1995 to 2001.
Ratio of Value of Imports to Exports by a Company Over the Years.
21.If the imports in 1998 was Rs. 250 crores and the total exports in the years 1998 and 1999 together was Rs. 500 crores, then the imports in 1999 was ?
A. Rs. 250 crores
B. Rs. 300 crores
C. Rs. 357 crores
D. Rs. 420 crores
E. Rs. 450 crores
Sol. D
The ratio of imports to exports for the years 1998 and 1999 are 1.25 and 1.40 respectively.Let the exports in the year 1998 = Rs. x crores.
Then, the exports in the year 1999 = Rs. (500 - x) crores.
1.25 = 250/x
x = 250/1.25 = 200 [ Using ratio for 1998 ]
Thus, the exports in the year 1999 = Rs. (500 - 200) crores = Rs. 300 crores.
Let the imports in the year 1999 = Rs. y crores.
Then, 40 = y/300
y = (300 * 1.40) = 420
Imports in the year 1999 = Rs. 420 crores.
22. The imports were minimum proportionate to the exports of the company in the year ?
A. 1995
B. 1996
C. 1997
D. 2000
E. 1998
Sol. C
The imports are minimum proportionate to the exports implies that the ratio of the value of imports to exports has the minimum value.
Now, this ratio has a minimum value 0.35 in 1997, i.e., the imports are minimum proportionate to the exports in 1997.
23. What was the percentage increase in imports from 1997 to 1998 ?
A. 72
B. 56
C. 28
D. Data Inadequate
E. 30
Sol. D
The graph gives only the ratio of imports to exports for different years. To find the percentage increase in imports from 1997 to 1998, we require more details such as the value of imports or exports during these years.
Hence, the data is inadequate to answer this question.
24. If the imports of the company in 1996 was Rs. 272 crores, the exports from the company in 1996 was ?
A. Rs. 370 crores
B. Rs. 320 crores
C. Rs. 280 crores
D. Rs. 275 crores
E. Rs. 300 crores
Sol. B
Ratio of imports to exports in the year 1996 = 0.85.
Let the exports in 1996 = Rs. x crores.
Then , 272/x = 0.85
x = 272/0.85 = 320
Exports in 1996 = Rs. 320 crores.
25. In how many of the given years were the exports more than the imports ?
A. 1
B. 2
C. 3
D. 4
E. 5
Sol. The exports are more than the imports imply that the ratio of value of imports to exports is less than 1.
Now, this ratio is less than 1 in years 1995, 1996, 1997 and 2000.
Thus, there are four such years.
Direction (26-30): Study the following graph carefully and answer the questions given below it.
26. What is the total number of students studying B.Sc in all the colleges together?
(1) 1825
(2) 1975
(3) 1650
(4) 1775
(5) None of these
Sol. (3)
Let the amount of Royalty to be paid for these books be Rs. r.
Then, 20 : 15 = 30600 : r
r = Rs. 22,950
27. What is the respective ratio of total number of students studying B.Sc. in the Colleges C and E together to those studying B.A. in the Colleges A and B together?
(1) 24 : 23
(2) 25 : 27
(3) 29 : 23
(4) 29: 27
(5) None of these
Sol. (3)
Central angle corresponding to Royalty = (15% of 360)º
[(15/100) *360] = 54
28. What is the respective ratio of total number of students studying B.Sc., B.A. and B. Com in all the colleges together?
(1) 71 : 67 : 75
(2) 67 : 71 : 75
(3) 71 : 68 : 75
(4) 75 : 71 : 68
(5) None of these
Sol. (2)
Clearly, marked price of the book = 120% of C.P.
Also, cost of paper = 25% of C.P
Let the cost of paper for a single book be Rs. n.
Then, 120 : 25 = 180 : n
n = Rs. 37. 50
29. Number of students studying B.Com. in College C forms approximately what per cent of the total number of student studying B. com in all the Colleges together?
(1) 39%
(2) 21%
(3) 44%
(4) 33%
(5) 17%
Sol. (1)
For the publisher to earn a profit of 25%, S.P. = 125% of C.P.
Also Transportation Cost = 10% of C.P
Let the S.P. of 5500 books be Rs. x.
Then, 10 : 125 = 82500 : x.
x = Rs. [(125 x 82500) x 10]= Rs. 1031250
S.P. of one book = Rs. (1031250/ 5500)= Rs. 187.50
30. Number of students studying B. A. in College B forms what per cent of total number of students studying all the disciplines together in that college? ( Rounded off to two digits after decimal)
(1) 26.86
(2) 27.27
(3) 29.84
(4) 32.51
(5) None of these
Sol. (4)
Printing Cost of book = 20% of C.P.
Royalty on book = 15% of C.P.
Difference = (20% of C.P.) - (15% of C.P) = 5% of C.P.
Percentage difference = [ (Difference/Printing) * 100%
= [ ( 5% of C.P./Printing Cost ) x 100%]
= 25%.
Directions(31-35) : Simplify the below given equations to find the unknown :
31. (50)3 ÷ (25)2 + 2466 = ?
B. 2654
C. 2456
D. 2342
E. None of these
Sol. (50×50×50)/(25×25) = 200
200+2466 = 2666.
32. (7.84)1/2 × (47.61)1/2 – 92161/2 = ?
B. - 78.86
C. - 76.68
D. -78.68
E. None of these
Sol. = 2.8 ×6.9 – 96
= 19.32 – 96
= – 76.68
33. 1235 .05÷125 × 32.03 + 0.04 = ?
A. 5642.9
B. 6574.8
C. 374.41
D. 317.14
B. 6574.8
C. 374.41
D. 317.14
E. None of these
Sol. 9.9 × 32.03+0.04 = 317.14
34. (15.25) 2 + (0.50)2 – (65.65)2 + (26.67)2 – (18.98)2 = ?
A. -6543
B. -4567
C. -3726
D. -3278
B. -4567
C. -3726
D. -3278
E. None of these
Sol. 232.56+0.25- 4310 + 711.29 – 360.24 = -3726.14
35. (13824)1/3 + (5776)1/2 =x2
A. 20
B. 100
C. 15
D. 10
B. 100
C. 15
D. 10
E. None of these
Sol. 24+76 = 100.
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