Directions ( 1 – 5): In the following questions, there are two equations in x and y. You have to solve both the equations and give the answer –
(a) if x > y
(b) if x < y
(c) if x ≥ y
(d) if x ≤ y
(e) if x = y or there is no relation between x and y
1. Question
I. 2x² – 3x + 1 = 0
II. 2y² – 5y + 3 = 0
Answer- D
Explanation:-
2x² – 3x + 1 = 0
=> 2x² – 2x – x + 1 = 0
=> (2x – 1) ( x -1) = 0
:. x = 1, 1/2
2y² – 5y + 3 = 0
=> 2y² – 2y – 3y + 3 = 0
=> ( 2y -3)(y – 1) = 0
:. y = 1, 3/2
x ≤ y
2.Question
I. x² + 21x + 110 = 0
II. y² + 17y + 72 = 0
Answer :-B
Explanation:-
x² + 21x + 110 = 0
=> x² + 11x + 10x + 110 = 0
=> ( x + 10)(x + 11) = 0
:. x = -10, -11
y² + 17y + 72 = 0
=> y² + 8y + 9y +72 = 0
=> (y +8)(y+9) = 0
:. y = -8, -9
x<y
3.Question
I. x² = 4
II. y2 – 6y + 8 = 0
Answer – D
Explanation:-
x² = 4
x = 2, -2
y² – 6y + 8 = 0
=> y² – 4y – 2y + 8 = 0
=> (y-4)(y-2) = 0
:. y = 4, 2
x ≤ y
4.Question
I. x² + 9x -22 = 0
II. 2y² – 7y + 6 = 0
Answer:-E
Explanation:-
x² + 9x – 22 = 0
=> x² + 11x – 2x – 22 = 0
=> (x+11)(x-2) = 0
:. x = 2, -11
2y² – 7y + 6 = 0
=> 2y² – 4y – 3y + 6 = 0
=> ( 2y – 3)(y – 2) = 0
:. y = 2, 3/2
x = y or there is no relation between x and y.
5.Question
I. 6x² + 5x + 1 = 0
II. 15y² + 11y + 2 = 0
Answer :-E
Explanation:-
6x² + 5x + 1 = 0
=> 6x² + 3x + 2x + 1 = 0
=> ( 3x +1)(2x +1) = 0
:. x = -1/3, -1/2
15y² + 11y + 2 = 0
=> 15y² + 5y + 6y + 2 = 0
=> (5y + 2)(3y +1) = 0
:. y = -1/3, -2/5
x = y or there is no relation between x and y.
6. Question
Train A running at a speed of 36 km/hr crosses train B in 20 seconds. Find the speed of train B (in km/hr), if the sum of the length of trains A & B is 600 meters and both trains running in the opposite direction.
(a) 72 km/hr
(b) 54 km/hr
(c) 48 km/hr
(d) 108 km/hr
(e) 81 km/hr
Answer:- A
Explanation:-
Let, Speed of train B = x km/hr
Two trains are running in the opposite direction, so
Relative speed of two trains=( 36 + x) km/hr
Now,
(36+x) = 600/20 × 18/5
=> 36+ x = 108
=> x = 108 – 36
:. x = 72 km/hr
Thus, the speed of train B = 72 km/hr.
7. Question
A invests Rs. X in a business. After four months, B joined him with Rs. 2X and A double his investment. If at the end of the years total profit is Rs. 13950, then find the profit share of A?
(a) 7250 Rs.
(b) 7750 Rs.
(c) 8750 Rs.
(d) 6750 Rs.
(e) 7050 Rs.
Answer:-B
Explanation:-
profit = Investment × time
Profit ratio of A and B = (X * 4) + (2X * 8) : ( 2X * 8)
= (4X + 16X) : 16X
= 5 : 4
Profit share of A = 13950 × 5/9 = 7750
8.Question
A man invested an amount in two schemes in the ratio of 2 : 3 at the rate of 20% p.a. and 10% p.a. on compound interest respectively. If the man gets a total interest of Rs. 1208 after two years from both the schemes, the find amount invested by man?
(a) 6000 Rs.
(b) 4800 Rs.
(c) 5000 Rs.
(d) 4500 Rs.
(e) 4000 Rs.
Answer:-E
Explanation:-
Let, Amount invested in two schemes = 2x and 3x respectively.
We know, Compound interest for 2 years = 2r + r²/100
C.I for 20% = 2×20 + 20²/100 = 44%
C.I for 10% = 2×10 + 10²/100 = 21%
Now,
Interest on amount 2x = 2x * 44/100 = 22x/25
Interest on amount 3x = 3x * 21/100 = 63x/100
According to question,
22x/25 + 63x/100 = 1208
=> 151x/100 = 1208
=> x = (1208×100) / 151
:. x = 800
Thus, the amount invested by the man = (2x+3x) = 5×800 = 4000
9.Question
The sum of the length of a rectangle and the side of a square is 72 meters. If the perimeter of the rectangle is 84 meters and the breadth of the rectangle is 18 meters, then find the measurement of the side of the square (in meters).
(a) 48
(b) 36
(c) 54
(d) 60
(e) 30
Answer:-A
Explanation:-
Perimeter of rectangle = 2( length + breadth) = 2(L + B)
According to question,
2( L + B ) = 84
=> 2L + 2×18 = 84
=> 2L = 48
:. L = 24 m.
:. Side of the square = (72 – 24) = 48 m.
10. Question
The ratio of time taken by A, B & C to complete work alone is 4: 6 : 3 respectively. If all three together complete the work in 8 days, then find in how many days A alone completes three-fourth of the same work?
(a) 12 days
(b) 30 days
(c) 15 days
(d) 24 days
(e) 18 days
Answer:- E
Explanation:-
Let, the time is taken by A, B and C = 4x, 6x and 3x respectively.
LCM = 12x
We know,
Total work =total time × Efficiency.
Now,
Efficiency of A = 12x/4x = 3
Efficiency of B = 12x/6x = 2
Efficiency of C = 12x/3x = 4
Total work = 8 × (3+2+4) = 72
3/4 work of 72 = 72× 3/4 = 54
Thus, the Time is taken by A to complete 3/4th of total work = 54/3 = 18 days.
11. Question
The population of a village decreased by 10% in the first year and then increased by 20% in the second year. Find the population of the village at the end of the second year if two years ago it was
15,000?
(a) 16180
(b) 16200
(c) 16320
(d) 16360
(e) 16480
Answer:-B
Explanation:-
Effective change = -10 + 20 – (10×20)/100
= 10 – 2 = 8%.
Required population increased = 15000 × 108/100 = 16200
12.Question
A shopkeeper marked up a shirt 50% above the cost price and allows successive discounts of 11(1/9)% and 10% on it. If the difference between the profit earned and the discount given is Rs. 200 then find the marked price of the shirt?
(a) Rs. 2100
(b) Rs. 3000
(c) Rs. 2400
(d) Rs. 3600
(e) Rs. 3300
Answer:-B
Explanation:-
(+) 50% = 1/2 CP = 2 : SP = 3
(-) 11(1/9)% = 1/9 CP = 9 : SP = 8
(-) 10% = 1/10 CP = 10 : SP = 9
=> CP = 5 : SP = 6
Now, CP : SP : MP
5 : 6 : 7.5 ( MP = 50% more of 5)
Here, Profit = ( SP – CP) = 1
Discount = ( MP – SP) = 1.5
According to question,
(1.5 – 1) unit = 200
0.5 unit = 200
1 unit = 400
:. 7.5 unit = (400 ×7.5) = 3000
Thus, the marked price of the shirt = 3000.
13. Question
The downstream speed of a boat is 5 km/hr more than its upstream speed and the ratio of the speed of the boat in still water to the speed of the stream is 19: 5. Find the total time taken by boat to travel 42 km downstream and 31.5 km upstream?
(a) 7 ½ hr
(b) 8 hr
(c) 9 hr
(d) 9 ½ hr
(e) 10 hr
Answer:-B
Explanation:-
Let,
Speed of boat = 19x
Speed of stream = 5x
Speed of downstream = (19x + 5x) = 24x
Speed of upstream = (19x – 5x) = 14x
According to question,
24x – 14x = 5
=> 10x = 5
:. x = 1/2
Now,
Speed of downstream = 24×1/2 = 12 km/hr
Speed of upstream = 14 × 1/2 = 7 km/hr
time taken in downstream = 42/12 = 3.5 hrs
Time taken in upstream = 31.5/7 = 4.5 hrs
Thus,required time =( 3.5+4.5) = 8 hrs
14. Question
A container contains a mixture of two liquids P and Q in the ratio 5 : 3. If 16 litres of the mixture is taken out and replaced with liquid Q, then the new ratio of liquid P to liquid Q becomes 1: 1. Find the initial quantity of mixture in the container.
(a) 80 L
(b) 60 L
(c) 70 L
(d) 48 L
(e) 96 L
Answer:-A
Explanation:-
Let,
In initial mixtures,
Quantity of P = 5x
Quantity of Q = 3x
After 16 lit of mixture is taken out,
Quantity of P = 5x – 5/8× 16 = 5x – 10
Quantity of Q = 3x -3/8 × 16 = 3x – 6 + 16 ( adding 16 lit Q)
Now, According to the question,
(5x – 10)/(3x +10) = 1/1
=> 5x – 10 = 3x + 10
=> 2x = 20
:. x = 10
Thus, initial mixture = (5x+3x) = 8×10 = 80 lit.
15. Question
The ratio of the present age of A to B is 8: 5 and the average of the present age of B and C is 35 years.If five years ago, the sum of ages of A and B is 55 years, then find the difference between the present age of A and C.
of A and C.
(a) 12 years
(b) 5 years
(c) 9 years
(d) 8 years
(e) 4 years
Answer:-B
Explanation:-
Let,
Age of A = 8x
Age of B = 5x
Total age of (B + C) = 35×2 = 70
Age of C = (70 – 5x)
Present age of (A+B) = 55 + 10 = 65
8x + 5x = 65
=> 13x = 65
:. x = 5
Present Age of A = 8x =8×5 = 40
Present age of C = 70 – 5×5 = 45
Thus, difference between present age of A and C
= ( 45 – 40 ) = 5 years.
Direction (16 – 20): The line graph given below shows the total number of posts (Photos + Videos) shared by six (A, B, C, D, E & F) people in December 2019. Read the data carefully and answer the questions.
16. Question
The total post shared by C is what per cent less than the total post shared by D?
(a) 20%
(b) 25%
(c) 15%
(d) 10%
(e) 30%
Answer:-A
Explanation:-
C = 32
D = 40
Required less percent = (40 – 32)/40 × 100 % = 20%
17. Question
In January 2020 total posts shared by B & F is 12 and 15 more than the previous month respectively, then find the total number of posts shared by B & F in January 2020?
(a) 95
(b) 91
(c) 93
(d) 97
(e) 99
Answer:-C
Explanation:-
Total post shared by B in 2020 = (28+12) = 40
Total post shared by F in 2020 = (38+15) = 53
Thus,total no of post shared by B & F in January 2020 = (40+53) = 93.
18. Question
Find the average number of posts shared by A, C & F?
(a) 42
(b) 48
(c) 40
(d) 36
(e) 44
Answer:-C
Explanation:-
Total number of post shared by A,C and F =(50+32+38) = 120
Thus,required average = 120/3 = 40
19. Question
The total photos shared by E is four more than the total videos shared by him, then find the total videos shared by E?
(a) 24
(b) 20
(c) 28
(d) 22
(e) 30
Answer:-B
Explanation:-
Let, video shared by E = x
Photos shared by E = x + 4
Now,
x + (x +4) = 44
=> 2x = 40
:. X = 20
:. Total video shared by E= 20.
20. Question
If the ratio of total photos to total videos shared by B is 5: 9, then find the total photos shared by B?
(a) 10
(b) 18
(c) 12
(d) 14
(e) 16
Answer:-A
Explanation:-
Let , photos shared = 5x & video shared = 9x
Now,
5x + 9x = 28
=> 14x = 28
:. x = 2
:. Photos shared by B = 5x =(5×2) = 10
Direction (21 – 35):- What will come in the place of question mark in following questions.
21.Question
(? ÷ 5 ÷ 7) × 14 + 112 = 420
(a) 710
(b) 720
(c) 660
(d) 770
(e) 750
Answer- D
Explanation:-
(? ÷ 5 ÷ 7) × 14 + 112 = 420
=> ? × 1/5 × 1/7 × 14 = 420 – 112
=> ? × 2/5 = 308
=> ? = 308 × 5/2
:. ? = 770
22.Question
(? ) ^(4 ×16 ÷32+1) + 12² = 360
(a) 4
(b) 6
(c) 8
(d) 2
(e) 3
Answer:-B
Explanation:-
(? ) ^(4 ×16 ÷32+1) + 12²= 360
=> (?)(2+1) = 360 – 144
=> ? ³ = 216
:. ? = 6
23.Question
50% of 128 + √16/2 × 4 =? +10
(a) 64
(b) 62
(c) 60
(d) 56
(e) 82
Answer:-B
Explanation:-
50% of 128 + √16/2 × 4 =? +10
=> 64 + 8 = ? + 10
:. ? = 62
24.Question
³√1331/11 + √81+? = 27
(a) 19
(b) 18
(c) 17
(d) 16
(e) 15
Answer:-C
Explanation:-.
³√1331/11 + √81+? = 27
=> 11/11 + 9 + ? = 27
=> 10 + ? = 27
:. ? = 17
25.Question
(14)² + 179 + (5)² = (?)²
(a) 10
(b) 20
(c) 30
(d) 40
(e) 22
Answer:-B
Explanation:-
(14)² + 179 + (5)² = (?)²
=> 196 + 179 + 25 = ?²
=> ? = √400
:. ? = 20
26. Question
28.5× 34 + 2320 ÷ 8 = (36)² – ?
(a) 51
(b) 47
(c) 43
(d) 34
(e) 37
Answer:-E
Explanation:-
28.5 × 34 + 2320 ÷ 8 = (36)² – ?
=> 969 + 290 = 1296 – ?
=> ? = 1296 – 1259
:. ? = 37
27.Question
47× 27 + 15600 ÷ 8 + 181 = ?
(a) 3320
(b) 3420
(c) 3370
(d) 3400
(e) 3460
Answer- D
Explanation:-
47× 27 + 15600 ÷ 8 + 181 = ?
=> 1269 + 1950 + 181 = ?
:. ? = 3400
28.Question
112.5× 5 + 4560 ÷ 6 − 175 × 7 = ?
(a) 103.5
(b) 91.5
(c) 97.5
(d) 110.5
(e) 115.5
Answer:-C
Explanation:-
112.5 × 5 + 4560 ÷ 6 − 175 × 7 = ?
=> 562.5 + 760 – 1225 = ?
:. ? = 97.5
29.Question
80% of ? = √(250 × 44 + 40% of 8500)
(a) 80
(b) 120
(c) 150
(d) 180
(e) 240
Answer:-C
Explanation:-
80% of ? = √(250 × 44 + 40% of 8500)
=> 4/5 × ? = √( 11000 + 3400)
=> 4/5 × ? = √14400
=> ? = 120 × 5/4
:. ? = 150
30.Question
? × 40 ÷ 24 × 27 = 594/115 × 2300/264
(a) 1
(b) 2
(c) 3
(d) 4
(e) 5
Answer:-A
Explanation:-
? × 40 ÷ 24 × 27 = 594/115 × 2300/264
=> ? × 40 × 1/24 × 27 = 45
=> ? = 45 × 24 × 1/40×1/27
:. ? = 1
31.Question
? + 13× 50 = 420 + 45% of 800 + 220
(a) 300
(b) 350
(c) 400
(d) 450
(e) 250
Answer:B-
Explanation:-.
? + 13× 50 = 420 + 45% of 800 + 220
=> ? + 650 = 420 + 360 + 220
=> ? = 1000 – 650
:. ? = 350
32.Question
12 % of ? + 12.5% of 960 = 16 × 12
(a) 840
(b) 960
(c) 800
(d) 600
(e) 400
Answer – D
Explanation:-
12 % of ? + 12.5% of 960 = 16 × 12
=> 3/25 × ? + 120 = 192
=> ? = 72 × 25/3
:. ? = 600
33.Question
15 × ? +20% of 450 = 360
(a) 12
(b) 20
(c) 24
(d) 16
(e) 18
Answer:-E
Explanation:-
15 × ? + 20% of 450 = 360
=> 15 × ? + 90 = 360
=> ? = 270/15
:. ? = 18
34.Question
75% of 3/4 × 8/9 × 1800 = ? + 600
(a) 300
(b) 400
(c) 250
(d) 480
(e) 540
Answer:-A
Explanation:-
75% of 3/4 × 8/9 × 1800 = ? + 600
=> 3/4 × 3/4 × 8/9 × 1800 – 600 = ?
:. ? = 300
35.Question
? % of 900 + 500 = 4 × 197
(a) 28
(b) 25
(c) 36
(d) 40
(e) 32
Answer:-E
Explanation:-
? % of 900 + 500 = 4 × 197
=> ?/100 × 900 + 500 = 788
=> ? × 9 = 788 – 500
=> ? = 288/9
:. ? = 32
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