Directions(1-5): In each question two equations are given, find x and y and give the answer:
A. x > y
B. x < y
C. x >= y
D. x =< y
E. x = y or relation can not be established.
1. (1) 8x^2 - 106x + 323 = 0
(2) 12y^2 - 109y + 247 = 0
Answer. x = 17/2 , 19/4
y = 13/3 , 19/4
Thus, x >= y.
2. (1) 4x + 7y = 42
(2) 3x - 11y = -1
Answer. x = 7
y = 2
Thus, x > y.
3. (1) 9x^2 - 29x + 22 = 0
(2) y^2 - 7y + 12 = 0
Answer. x = 2 , 11/9
y = 3 , 4
Thus, x < y.
4. (1) 3x^2 - 4x - 32 = 0
(2) 2y^2 - 17y + 36 = 0
Answer. x = 4 , -8/3
y = 4 , 9/2
Thus, x =< y
5. (1) 3x^2 - 19x - 14 = 0
(2) 2y^2 + 5y + 13 = 0
Answer. x = 7 , -2/3
y = -3/2 , -1
Thus, x > y.
6. A merchant purchases a wrist watch for Rs 450 and fixes its list price in such a way that after allowing a discount of 10%, he earns a profit of 20%. Find the list price ?
A. 550
B. 600
C. 500
D. 650
E. None of these
Sol. C.P. of wrist watch = Rs 450
Discount = 10%
Profit earned = 20%
Lets asssume list price to be = 'x'
Then,
450*(120/100) = x*(90/100)
Solving, x = Rs 600.
7. An article was sold at profit of 12%. If the C.P. would be 10% less and selling price is Rs 5.75 more then there would be 30% profit.Then at what price it should be sold to make a profit of 20% ?
A. Rs 136
B. Rs 138
C. Rs 140
D. Rs 135
E. None of these
Sol. Lets assume C.P. be 'x'
Then, S.P. will be = 1.12x ( as 12% profit)
Now, C.P. = 0.9X (as C.P. is reduuced by 10%)
S.P. = 1.12x + 5.75
Now as profit is 30%,
(130/100)*0.9x = 1.12x + 5.75
Solving, x = Rs 115
Now at 20% profit S.P. will be = (120/100)*115 = Rs 138.
8. Th simple interest on a sum of money is 8/25 of sum. If the number of years numerically is half the rate of interest then what is the rate of interest ?
A. 5
B. 4
C. 6
D. 8
E. None of these
Sol. Given, S.I. = (8/25)P
Time = t = R/2
Now, S.I.= PRT/100
(8/25)P = [P*R*(R/2)]/100
Solving, R = 6%.
9. Three glasses of equal volume contain acid mixed with water. The ratio of acid and water are 2:3, 3:4 and 4:5 respectively. Contents of these glasses are poured in a large vessel. The ratio of acid and water in the large vessel is :
A. 417:564
B. 401:544
C. 407:560
D. 411:540
E. None of these
Sol. Glass 1, acid = 2x ; water = 3x
Glass 2, acid = 3y ; water = 4y
Glass 3, acid = 4z ; water = 5z
New Glass composition, acid:water = (2x+3y+4z):(3x+4y+5z)
Also as the volumes of glasses are equal thus,
2x+3x = 3y+4y
5x = 7y
y = 5x/7
Also, 2x+3x = 4z+5z
5x = 9z
z = 5x/9
Putting these values above, 401:544.
10. The average weight of 36 students is 50 kg. If was found later that the weight of one of the student was misread as 73 kg, whereas his actual weight was 37 kg. Find the correct average weight(in kg).
A. 50
B. 49
C. 51
D. 47
E. 48
Sol. Sum of the weights/36 = 50
Sum of the weights = 50*36 = 1800
Correction in sum of the weights = 37 - 73 = -36
Correct sum of the weights = 1800 - 36 = 1764
Thus, correct average is = 1764/36 = 49.
11. Train takes 4 seconds to pass a man. Another train travelling in opp. direction of same length takes 5 seconds to pass the man. Find the time taken by both trains to cross each other ?
A. 51/9 sec
B. 40/9 sec
C. 42/9 sec
D. 41/9 sec
E. None of these
Sol. Length of trains = x meter
Speed of 1st train = x/4 m/sec
Speed of 2nd train = x/5 m/sec
Relative speed = x/4 + x/5 = 9x/20 m/sec
Required Time = 2x/(9x/20) = 40/9 seconds.
12. One third of a certain journey is covered at the rate of 25 km/hr, one fourth at the rate of 30 km/hr and the rest at 50 km/hr. Find the average speed of the whole journey ?
A. 100/3
B. 35
C. 30
D. 37
E. None of these
Sol. Lets assume the total distance to be 'd'.
The, average speed = d/[(d/3*25)+(d/4*30)+(5d/12*50)] = 100/3 km/hr.
13. 8 men and 6 women can complete a work in 6 days. 1 man works twice as much as 1 woman in a day. 8 men and 4 women started working, after 2 days 4 men left and 4 new women joined. In how many more days will the work be completed ?
A. 6
B. 7
C. 5
D. 4
E. None of these
Sol. (8M + 4W)6 = T
Also, M = 2W
Thus, (16W + 4W)*6 = T
120W = T
and 60M = T
Now, (8M + 4W)*2 + (4M + 8W)*t = T
(8M + 2M)*2 + (4M + 4M)*t = 60M
20 + 8t = 60
t = 5 days.
14. A motor boat travelling at the same speed can cover 25 km upstream and 39 km downstream in 8 hrs. At the same speed, it can cover 35 km upstream and 52 km downstream in 11 hrs. Find the speed of the stream ?
A. 5
B. 6
C. 4
D. 3
E. None of these
Sol. Lets assume upstream speed to be 'x' km/hr
And downstream speed to be 'y' km/hr
Then, 25/x + 39/y = 8
And, 35/x + 52/y = 11
Solving these two,we get,
x = 5km/hr
y = 13 km/hr
Thus, speed of stream = (y - x)/2 = (13 - 5)/2 = 4 km/hr.
15. In a lab, 2 bottles contain mixture of acid and water in the ratio of 2:5 in 1st and 7:3 in 2nd. Find the ratio in which these two should be mixed so that the new ratio will become 2:3 ?
A. 21:8
B. 15:8
C. 9:8
D. 19:8
E. None of these
Sol. Using the allegation method, (3/10):(4/35) = 21:8.
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