Directions (1-5): In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer
(1) if x > y
(2) if x >=y
(3) if x < y
(4) if x <=y
(5) if x = y or relationship between x and y cannot be established.
1. 1) 8x^2 -10x +3 = 0
2) 7y^2 -17y +6 = 0
Sol. For 1st eqn values are,
x = 0.5, 0.75
For 2nd equation values are,
y = 2, 3/7
Thus, no relation between the two.
2. 1) 4x^2 -13x +3 = 0
2) 2y^2 -13y +21 = 0
Sol. For 1st eqn values are,
x = 3, 1/4
For 2nd equation values are,
y = 3, 7/2
Thus, y >= x.
3. 1) 5x^2 -32x +12 = 0
2) y^2 -15y +56 = 0
Sol. For 1st eqn values are,
x = 6, 2/5
For 2nd equation values are,
y = 8, 7
Thus, y > x.
4. 1) 2x^2 +9x +10 = 0
2) 5y^2 +19y +18 = 0
Sol. For 1st eqn values are,
x = -2, -5/2
For 2nd equation values are,
y = -2, -9/5
Thus, y >= x.
5. 1) x^2 +11x +28 = 0
2) y^2 +16y +64 = 0
Sol. For 1st eqn values are,
x = -7, -4
For 2nd equation values are,
y = -8
Thus, x > y.
6. 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 %.
7. What is the area of the square whose side is equal to the side of an equilateral triangle with area 9*(3)^0.5 ?
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)^0.5,thus,
[a*a*(3)^0.5]/2 = 9*(3)^0.5
a = 6
Thus area of the square,
= a^2
= (6)^2
= 36
8. 6 yrs ago, ratio of age of Annu and Nalini was 7:4. The age of Annu 4 yrs hence is equal to age of Nalini 10 yrs hence. Then find the sum of ages of both 2 yrs from now ?
A. 38
B. 36
C. 34
D. 32
E. None of these
Sol. Lets assume Annu's age to be 'x'
And Nalini's age to be 'y'
The 1st eqn. will be,,
(x-6)/(y-6) = 7/4
The 2nd eqn. will be,
x + 4 = y + 10
Solving both, we get,
x = 20
y = 14
Thus, 20 + 14 + 4 = 38.
9. 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.
10. 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
11. 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.
12. A certain amount of money is invested in a scheme offering 12% simple per annum. After 2 yrs the total amount obtained from this scheme is invested for 5 yrs in another scheme offering 20% simple per annum. If the total amount obtained is 29,760. Then find the sum of money invested initially.
A. 10000
B. 12000
C. 13000
D. 15000
E. None of these
Sol. Let initial sum = 100
100*(124/100)*[(20*5)+100]/100 = 248 rs
For 248 rs total amount = Rs 29760
Thus, for 100 rs total amount will be = 12000 rs.
13. 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.
14. 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.
15. A sells a horse to B for Rs 4860, thereby losing 19%, B sells it to C at a price which would have given A 17% profit. Find B's gain.
A. Rs 2160
B. Rs 2610
C. Rs 1260
D. Rs 2260
E. None of these
Sol. C.P. for A = 4860*[100/(100-19)] = 6000
S.P. with 17% profit for A = 6000*[(100+17)/100] = 7020
B's gain = 7020 - 4860 = 2160.
Directions(16-20):Find the missing numbers in the given series
16. 11, 14, 23, 50, _
A. 130
B. 132
C. 131
D. 133
E. None of these
Sol. 11 + 3 = 14
14 + 3^2=23
23 + 3^3=50
Thus, 50 + 3^4 = 131
17. 19, 25, 42, 71, 113, _
A. 149
B. 156
C. 169
D. 175
E. None of these
Sol. The difference of the difference is in the A.P.
= 113 + 56
= 169.
18. 35, 30, 44, 39, _
A. 60
B. 55
C. 54
D. 53
E. None of these
Sol. 21 + 14 = 35
35 - 5 = 30
30 + 14 = 44
44 - 5 = 39
Thus, 39 + 14 = 53
19. 23, 39, 32, 48, 41, _
A. 56
B. 57
C. 55
D. 54
E. 52
Sol. 23 + 16 = 39
39 - 7 = 32
32 + 16 = 48
48 - 7 = 41
Thus, 41 + 16 = 57.
20. 13, 17, 33, 97, _
A. 243
B. 341
C. 353
D. 281
E. None of these
Sol. 13 + 4 = 17
17 + 4^2=33
33 + 4^3=97
Thus, 97 + 4^4 = 353.
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