1. Which of the following equations has real roots ?
A. (x - 1)(2x - 5) = 0
B. [latex]{x}^{2} [/latex] + x + 4 = 0
C. 2[latex]{x}^{2} [/latex] - 3x + 4 = 0
D. 3[latex]{x}^{2} [/latex] + 4x + 5 = 0
E. None of these
Answer: A
Explanation:
Given equation (x - 1)(2x - 5) = 0
[latex]\Rightarrow 2{x}^{2} - 7x + 5 = 0[/latex]
i.e, D = [latex]{(-7)}^{2} - 4 \times 2 \times 5 [/latex] = (49 - 40) = 9 > 0
i.e, Given equation has real roots.
2. For what values of k, the equation [latex]{x}^{2} [/latex] + 2(k - 4)x + 2k = 0 has equal roots ?
A. 6, 4
B. 10, 4
C. 8, 2
D. 12, 2
E. None of these
Answer: C
Explanation:
Since the roots are equal, we have D = 0
i.e, 4[latex]({k - 4})^{2} [/latex] - 8k = 0 [latex]\Rightarrow [/latex] [latex]({k - 4})^{2} [/latex] - 2k = 0
[latex]{k}^{2} [/latex] + 16 - 10k = 0 [latex]{k}^{2} [/latex] - 10k + 16 = 0
[latex]\Rightarrow [/latex] (k - 8) (k - 2) = 0 [latex]\Rightarrow [/latex] k = 8 or k =2
3. If a and b are the roots of the equation [latex]{x}^{2} [/latex] - 6x + 6 = 0, then the value of ([latex]{a}^{2} [/latex] + [latex]{b}^{2} [/latex] ) are :
A. 6
B. 12
C. 24
D. 36
E. None of these
Answer: C
Explanation:
(a + b) = 6 and ab = 6
i.e, ([latex]{a}^{2} [/latex] + [latex]{b}^{2} [/latex] ) = [latex]{(a + b)}^{2} [/latex] - 2ab = [latex]{6}^{2} - 2 \times 6[/latex] = (36 - 12 ) = 24
4. 120.001 × 45.995 + 145.002 + 14.995 ÷ 4.995
A. 5440
B. 5670
C. 6450
D. 6240
E. None of these
Answer: B
Explanation:
120 × 46 + 145 + 15 ÷ 5
= 5520 + 145 + 3
= 5668
= 5670(approx.)
5. 125.0046 ÷ 24.9982 + 14.9985 = ? + 13.9985
A. 15
B. 145
C. 241
D. 6
E. None of these
Answer: D
Explanation:
125 ÷ 25 + 15 = x + 14
5 + 15 = x + 14
20 = x + 14
X = 20 - 14
X = 6
6. 65% of 9780.0245 - 48% of 499.982 = x + 25% of 9827.992
A. 4520
B. 3660
C. 3150
D. 2450
E. None of these
Answer: B
Explanation:
65% × 9780 - 48% × 500 = x + 9828 × 25%
= 6357 - 240 = x + 2457
= 6357 - 240 - 2457 = x
= X = 3660
7. The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
A. 3%
B. 4%
C. 5%
D. 6%
E. None of these
Answer: B
Explanation:
65[latex]\times (\frac {90}{100}) \times (\frac {(100 - x)}{100})[/latex] = 56.16
= 4%
8. A single discount equivalent to the discount series of 20%, 10% and 5% is?
A. 25%
B. 30%
C. 31.6%
D. 33.5%
E. None of these
Answer: C
Explanation:
100[latex]\times (\frac {80}{100}) \times (\frac {90}{100}) \times (\frac {95}{100})[/latex] = 68.4
100 - 64.4 = 31.6%
9. A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
A. 10%
B. 11%
C. 12%
D. 15%
E. None of these
Answer: C
Explanation:
Original price = 100
CP = 80
S = [latex]80 \times (\frac {140}{100})[/latex] = 112
100 - 112 = 12%
10. The average of five number is 42 ,if one number is excluded the average become 35.The excluded number is
A. 7
B. 40
C. 70
D. 20
E. None of these
Answer: C
Explanation:
[latex]\frac {x}{5} = 42 \Rightarrow 42 \times 5[/latex] = 210
[latex]\frac {x}{4} = 35 \Rightarrow 35 \times 4[/latex] = 140
210 - 140 = 70
11. The average age of 30 students in a class is 20 years. The average age of 25 students is 15. What is the average age of remaining students
A. 42
B. 54
C. 34
D. 45
E. None of these
Answer: D
Explanation:
Sum of age of 15 Students = [latex] (40 \times 20) - (25 \times 15) [/latex] = 600 - 375 = 225
Average = [latex] \frac {225}{5}[/latex] = 45
12. The average of nine number is x and the average of three of these is y if the average of the remaining three is z, then
A. [latex]3 x = y + z[/latex]
B. [latex]2 x = y + z[/latex]
C. [latex] x = 3 y + 3 z[/latex]
D. x = 4y +5z
E. None of these
Answer: A
Explanation:
[latex] x = \frac {3 y + 3 z}{9} \Rightarrow 3 x = y + z[/latex]
13. Ravi runs 200 metres in 24 seconds. Find his average speed :
A. 20 km/h
B. 24 km/h
C. 28.5 km/h
D. 30 km/h
E. None of these
Answer: Option D
Explanation:
Average speed = [latex]\frac {200} {24} * \frac {18}{5}[/latex] = 30 km/hr.
14. A man completes 30 km of a journey at 6 km/hr and the remaining 40 km of the journey in 5 hours his average speed for the whole journey is :
A. 6[latex]\frac {4} {11}[/latex] km/hr
B. 7 km/hr
C. 7[latex]\frac {1} {2}[/latex] km/hr
D. 8 km/hr
E. None of these
Answer: Option B
Explanation:
Average speed = [latex]\frac {30 + 40} {\frac {30}{6} + 5} = \frac {70}{10}[/latex] = 7 km/hr.
15. A train with a speed of 60 kmph crosses a pole in 30 seconds. The length of the train is
A. 500 m
B. 750 m
C. 900 m
D. 1000 m
E. None of these
Answer: Option A
Explanation:
Length of the train =60 * [latex]\frac {5} {18}[/latex] * 30 = 500 meter
16. Simple Interest on Rs. 500 for 4 years at 6.25% per annum is equal to the Simple Interest on Rs.400 at 5% per annum for a certain period of time. The period of time is
A. 4 years
B. 5 years
C. 6 [latex]\frac {1} {4}[/latex]
D. 8 [latex]\frac {2} {3}[/latex]
E. None of these
Answer - Option C
Explanation -
500 * 4 * 6.25% = 400 * 5 * t
t = 6.25 years
17. A sum becomes Rs. 2916 in 2 years at 8% per annum compound interest. The sum is
A. Rs. 2750
B. Rs. 2500
C. Rs. 2625
D. Rs. 2560
E. None of these
Answer - Option B
Explanation -
Let the required sum be Rs. x.
x * [latex]\frac {108} {100}[/latex] * [latex]\frac {108} {100}[/latex] = 2916
x = Rs. 2500
18. If 200 becomes 240 in 4 years, then the rate of simple interest per annum is
A. [latex]\frac {25} {6}[/latex]%
B. [latex]\frac {25} {3}[/latex]%
C. [latex]\frac {25} {2}[/latex]%
D. 5%
E. None of these
Answer - Option D
Explanation -
Given that Rs. 200 becomes Rs. 240 in 4 years, thus it would have become Rs. 210 at the end of first year.
Hence, rate of simple interest = [latex]\frac {10} {200}[/latex] * 100 = 5%
19. A sum of money doubles itself in 5 years when the interest is compounded annually. The number of years when it will become eight times is
A. 10
B. 12
C. 15
D. 20
E. None of these
Answer - Option C
Explanation -
The money gets doubled in 5 years which means it becomes twice of itself after every 5 years. Hence, it will be increased to 4 times in 10 years and 8 times in 15 years.
20. Compound interest on rupees 8000 for 1 year at 10% per annum compounded half yearly is
A. 800
B. 1680
C. 840
D. 736.20
E. None of these
Answer - Option D
Explanation -
8000 * [latex]\frac {209} {200} * \frac {209} {200}[/latex] = 8736.20
So, interest = 8736.20 − 8000 = 736.20
21. A man purchases some oranges @ Re. 1 for 6 and an equal number @ Re. 1 for 4. He mixed them and sold @ 20 paise each. His gain or loss in percent is
A. loss 5%
B. loss 4%
C. profit 5%
D. profit 4%
E. None of these
Answer - Option B
Explanation -
CP for 12 eggs = 2 ; SP (24 eggs) = 4.80
Now, [latex]\frac {CP (for 12 eggs)} {CP (for 24 eggs)}[/latex] = [latex]\frac {3} {5}[/latex]
i.e, % Loss = [latex]\frac {20} {5} * 100%[/latex] = 4%
22. By selling an article at Rs. 1250, a gain of 25% is made on the CP. At what price should the article be sold in order that a loss of 20% is made on the selling price ?
A. Rs. 800
B. Rs. 850
C. Rs. 833 [latex]\frac {1} {3}[/latex]
D. Rs. 833 [latex]\frac {2} {3}[/latex]
E. None of these
Answer - Option C
Explanation -
[latex]\frac {120} {100} = \frac {1250} {CP}[/latex]
CP = 1000
Now, 120% of SP = 1000,
SP = 833 [latex]\frac {1} {3}[/latex]
23. Rajan sold his watch for Rs. 75 and got a percentage of profit equal to the cost price. The cost price of the watch is
A. Rs. 40
B. Rs. 60
C. Rs. 50
D. Rs. 52.50
Answer - Option C
24. By selling 15 mangoes, a fruit seller gains the selling price of 3 mangoes. His gain is
A. 25%
B. 16%
C. 24%
D. 27%
Answer - Option A
Explanation -
[latex]\frac {3} {12} * 100%[/latex] = 25%
25. Ram sold a cow to Rahim at 20% profit . Rahim sold it to Robert at 25% profit. If Robert paid Rs. 900, then Ram had purchased the cow (in rupees) for
A. 600
B. 700
C. 750
D. 800
Answer - Option A
Explanation -
Let Ram’s cost price = Rs. 100
i.e, Ram’s selling price
= [latex] Rs.100 * \frac {100 + 20} {20}[/latex]
= Rs. 120
Rahim’s cost price = Rs. 120
i.e, Rahim’s selling price
= [latex] Rs.120 * \frac {100 * 25} {100}[/latex]
= Rs.150
Robert’s cost price = Rs. 150
If Robert’s cost price is Rs. 150, then Ram’s cost price = Rs. 100
Hence if Robert’s cost price is Rs. 900, then Ram’s cost price
= [latex] Rs.900 * \frac {100 } {150}[/latex] = Rs. 600
Direction (26-30): Refer to the following Line Graph and answer the given questions.
26. The number of people who traveled by Train B on Friday is 30% more than the people who traveled by the same train on Thursday. What is the respective ratio between the number of people who traveled on Friday and those who traveled on Saturday by the same train?
A. 14 : 15
B. 13 : 14
C. 15 : 16
D. 13 : 14
E. 13 : 16
Answer: Option E
Explanation:
30% of 200 = 60
People traveled by Train B on Friday = 260
260 : 320 = 13 : 16
27. What is the difference between the total number of people who traveled by Train B on Saturday and Sunday together and the total number of people who traveled by Train A on Saturday and Sunday together?
A. 20
B. 30
C. 10
D. 50
E. 40
Answer: Option C
Explanation:
Train B on Saturday and Sunday together = 320 + 310 = 630
Train A on Saturday and Sunday together = 350 + 270 = 620
Difference = 630 – 620 = 10
28. What is the average number of people traveling by Train B on Monday, Tuesday, Wednesday and Thursday?
A. 160.5
B. 130.5
C. 172.5
D. 165.5
E. 164.5
Answer: Option C
Explanation:
200 + 170 + 120 + 200 = 172.5
29. The number of people who traveled by Train A decreased by what percent from Saturday to Wednesday?
A. 30%
B. 60%
C. 30%
D. 42%
E. 33%
Answer: Option B
Explanation:
[[latex]\frac{(350 – 140)}{350}[/latex] ] × 100
= [[latex]\frac{210}{350}[/latex] ] × 100 = 60%
30. The total number of people who traveled by both the given trains together on Monday is approximately what percent more than the total number of people who traveled by both the given trains together on Wednesday?
A. 68%
B. 63%
C. 62%
D. 69%
E. 65%
Answer: Option D
Explanation:
[latex]\frac{(440 – 260)}{260}[/latex] × 100
= [latex]\frac{180}{260}[/latex] × 100
= 69%
Directions [31-35]: Study the following information carefully and answer the questions given below:
Classification of 100 Students Based on the Marks Obtained by them in Physics and Chemistry in an Examination.
Subject |
Marks out of 50 |
40 and above |
30 and above |
20 and above |
10 and above |
0 and above |
Physics |
9 |
32 |
80 |
92 |
100 |
Chemistry |
4 |
21 |
66 |
81 |
100 |
Average (Aggregate) |
7 |
27 |
73 |
87 |
100 |
31. What is the different between the number of students passed with 30 as cut-off marks in Chemistry and those passed with 30 as cut-off marks in aggregate?
A. 3
B. 4
C. 5
D. 6
E. 10
Explanation -
Required difference
= (No. of students scoring 30 and above marks in Chemistry) - (Number of students scoring 30 and above marks in aggregate)
= 27 - 21
= 6.
32. If at least 60% marks in Physics are required for pursuing higher studies in Physics, how many students will be eligible to pursue higher studies in Physics?
A. 27
B. 32
C. 34
D. 41
E. 45
Answer - Option B
Explanation -
We have 60% of 50 = [latex](\frac {60}{100} \times 50)[/latex] = 30
i.e, Required number
= No. of students scoring 30 and above marks in Physics
= 32
33. The percentage of number of students getting at least 60% marks in Chemistry over those getting at least 40% marks in aggregate, is approximately?
A. 21%
B. 27%
C. 29%
D. 31%
E. 45%
Answer - Option C
Explanation -
Number of students getting at least 60% marks in Chemistry
= Number of students getting 30 and above marks in Chemistry
= 21.
Number of students getting at least 40% marks in aggregate
= Number of students getting 20 and above marks in aggregate
= 73.
Required percentage = [latex](\frac {21}{73} \times 100)[/latex]%
= 28.77%
≈ 29%.
34. The number of students scoring less than 40% marks in aggregate is?
A. 13
B. 19
C. 20
D. 27
E. 25
Answer - Option D
Explanation -
We have 40% of 50 = [latex](\frac {40}{100} \times 50)[/latex] = 20
i.e, Required number
= Number of students scoring less than 20 marks in aggreagate
= 100 - Number of students scoring 20 and above marks in aggregate
= 100 - 73
= 27.
35. If it is known that at least 23 students were eligible for a Symposium on Chemistry, then the minimum qualifying marks in Chemistry for eligibility to Symposium would lie in the range?
A. 40-45
B. 30-40
C. 20-30
D. Below 20
E. Below 30
Answer - Option C
Explanation -
Since 66 students get 20 and above marks in Chemistry and out of these 21 students get 30 and above marks, therefore to select top 35 students in Chemistry, the qualifying marks should lie in the range 20-30.