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Question 1 of 10

1. Question

1 points

Category: Quantitative Aptitude

The speed of the stream is 6 km/hr and speed of the boat in still water is 9 km/hr. If a boat takes 70 hrs to travel downstream from point A to B and coming back to point C midway between A and B, the what is the total distance travelled by the boat?

Correct

Explanation:
Downstream speed = 9+6 = 15
Upstream speed = 9-6 = 3
Let the distance from A to B is x km
downstream distance = x, upstream distance is half of x because boat goes half way upstream, then
x/15 + (x/2)/3 = 70
solve, x = 300
so boat covered 300 + 300/2

Incorrect

Explanation:
Downstream speed = 9+6 = 15
Upstream speed = 9-6 = 3
Let the distance from A to B is x km
downstream distance = x, upstream distance is half of x because boat goes half way upstream, then
x/15 + (x/2)/3 = 70
solve, x = 300
so boat covered 300 + 300/2

Question 2 of 10

2. Question

1 points

Category: Quantitative Aptitude

A cone of radius 12 cm and height 9 cm is mounted on a cylinder of radius 12 cm and height 4 cm. What is the total surface area of the figure thus formed?

Correct

Explanation:
Slant height of cone, l = √9^{2} + 12^{2} = 15 cm
Total surface area of final figure = curved surface area of cone + curved surface area of cylinder + area of base
= ᴨrl + 2ᴨrh + ᴨr^{2}
= ᴨr (l + 2h + r)
= (22/7) * 12 * (15 + 2*4 +12)

Incorrect

Explanation:
Slant height of cone, l = √9^{2} + 12^{2} = 15 cm
Total surface area of final figure = curved surface area of cone + curved surface area of cylinder + area of base
= ᴨrl + 2ᴨrh + ᴨr^{2}
= ᴨr (l + 2h + r)
= (22/7) * 12 * (15 + 2*4 +12)

Question 3 of 10

3. Question

1 points

Category: Quantitative Aptitude

Age of Ruhan is 5 years less than that of Aditya and also Ruhan’s age is 7 years more than Pihu. After 7 years, the ratio of ages of Aditya to Pihu’s will be 8 : 5. What was the age of Ruhan 2 years ago?

Correct

Explanation:
R = A-5
R = P+7
(A+7)/(P+7) = 8/5
Or (R+5+7) / (R- 7+7) = 8/5
Solve, R = 20
So R-2 = 18

Incorrect

Explanation:
R = A-5
R = P+7
(A+7)/(P+7) = 8/5
Or (R+5+7) / (R- 7+7) = 8/5
Solve, R = 20
So R-2 = 18

Question 4 of 10

4. Question

1 points

Category: Quantitative Aptitude

A bag contains 4 red, 3 yellow and 5 green balls. Find the probability of drawing 4 balls in which there are exactly half green balls.

Correct

Explanation:
Exactly half green means 2 green out of total 4 balls to be drawn.
So 2 green out of 5 green balls should be selected and other 2 any of (4+3) red and yellow balls
Prob = ^{5}C_{2} × ^{7}C_{2} / ^{12}C_{4}

Incorrect

Explanation:
Exactly half green means 2 green out of total 4 balls to be drawn.
So 2 green out of 5 green balls should be selected and other 2 any of (4+3) red and yellow balls
Prob = ^{5}C_{2} × ^{7}C_{2} / ^{12}C_{4}

Question 5 of 10

5. Question

1 points

Category: Quantitative Aptitude

A and B started a business with investing Rs 4000 and Rs 6000 respectively. After 4 months A withdrew Rs 400 while B added Rs 400 and C also joined them with Rs 8000. After a year, what will be the ratio of their shares out of total profit?

Directions (6-10): In the following questions, two equations numbered I and II are given. You have to solve both the equations and give answer –

x^{2} + 15x + 54 = 0, 2y^{2} – 21y + 55 = 0

Correct

Explanation:
x^{2} + 15x + 54 = 0
x^{2} + 9x + 6x + 54 = 0
Gives x = -9, -6
2y^{2} – 21y + 55 = 0
2y^{2} – 10y – 11y + 55 = 0
Gives y = 5, 11/2
Put on number line
-9……. -6….. 5…… 11/2

Incorrect

Explanation:
x^{2} + 15x + 54 = 0
x^{2} + 9x + 6x + 54 = 0
Gives x = -9, -6
2y^{2} – 21y + 55 = 0
2y^{2} – 10y – 11y + 55 = 0
Gives y = 5, 11/2
Put on number line
-9……. -6….. 5…… 11/2

Question 7 of 10

7. Question

1 points

Category: Quantitative Aptitude

Directions (6-10): In the following questions, two equations numbered I and II are given. You have to solve both the equations and give answer –

8x^{2} – 2x – 3 = 0, 4y^{2} + 12y + 5 = 0

Correct

Explanation:
8x^{2} – 2x – 3 = 0
8x^{2} + 4x – 6x – 3 = 0
Gives x = -1/2, 3/4
4y^{2} + 12y + 5 = 0
4y^{2} + 2y + 10y + 5 = 0
Gives y = -1/2, -5/2
Put on number line
-5/2…… -1/2 ….. 3/4

Incorrect

Explanation:
8x^{2} – 2x – 3 = 0
8x^{2} + 4x – 6x – 3 = 0
Gives x = -1/2, 3/4
4y^{2} + 12y + 5 = 0
4y^{2} + 2y + 10y + 5 = 0
Gives y = -1/2, -5/2
Put on number line
-5/2…… -1/2 ….. 3/4

Question 8 of 10

8. Question

1 points

Category: Quantitative Aptitude

Directions (6-10): In the following questions, two equations numbered I and II are given. You have to solve both the equations and give answer –

2x^{2} + x – 21 = 0, 2y^{2} + 11y + 14 = 0

Correct

Explanation:
2x^{2} + x – 21 = 0
2x^{2} – 6x + 7x – 21 = 0
Gives x = -7/2, 3
2y^{2} + 11y + 14 = 0
2y^{2} + 4y + 7y + 14 = 0
Gives y = -7/2, -2
Put on number line
-7/2… -2……. 3
When y = -2, y < x(3) and y > x(-7/2) so cant be determined

Incorrect

Explanation:
2x^{2} + x – 21 = 0
2x^{2} – 6x + 7x – 21 = 0
Gives x = -7/2, 3
2y^{2} + 11y + 14 = 0
2y^{2} + 4y + 7y + 14 = 0
Gives y = -7/2, -2
Put on number line
-7/2… -2……. 3
When y = -2, y < x(3) and y > x(-7/2) so cant be determined

Question 9 of 10

9. Question

1 points

Category: Quantitative Aptitude

Directions (6-10): In the following questions, two equations numbered I and II are given. You have to solve both the equations and give answer –

2x^{2} – 7x ¬+ 3 = 0, 4y^{2} – 27y + 18 = 0

Correct

Explanation:
2x^{2} – 7x ¬+ 3 = 0
2x^{2} – x – 6x ¬+ 3 = 0
Gives x = 1/2, 3
4y^{2} – 27y + 18 = 0
4y^{2} – 27y + 18 = 0
Gives y = 3/4, 6
Put on number line
1/2…………. 3/4………. 3……… 6

Incorrect

Explanation:
2x^{2} – 7x ¬+ 3 = 0
2x^{2} – x – 6x ¬+ 3 = 0
Gives x = 1/2, 3
4y^{2} – 27y + 18 = 0
4y^{2} – 27y + 18 = 0
Gives y = 3/4, 6
Put on number line
1/2…………. 3/4………. 3……… 6

Question 10 of 10

10. Question

1 points

Category: Quantitative Aptitude

Directions (6-10): In the following questions, two equations numbered I and II are given. You have to solve both the equations and give answer –

x^{2} – 11x + 18 = 0, y^{2} + 10y + 24 = 0

Correct

Explanation:
x^{2} – 11x + 18 = 0
x^{2} – 2x – 9x + 18 = 0
Gives x = 2, 9
y^{2} + 10y + 24 = 0
y^{2} + 6y + 4y + 24 = 0
Gives y= -6 , -4
Put on number line
-6……….. -4……. 2…….9

Incorrect

Explanation:
x^{2} – 11x + 18 = 0
x^{2} – 2x – 9x + 18 = 0
Gives x = 2, 9
y^{2} + 10y + 24 = 0
y^{2} + 6y + 4y + 24 = 0
Gives y= -6 , -4
Put on number line
-6……….. -4……. 2…….9