# SBI Clerk Mains Quantitative Aptitude (Day-43)

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Application Sums

1) Ratio of the mixture of milk and water in the ratio of Vessel A is 5: 3. If Vessel B contains the quantity of water is 20 liters and vessel C contains 30 liters of milk. If half of the mixture of vessel A is poured into Vessel B, then the mixture of vessel B is poured into vessel C and then finally vessel C mixture is poured into vessel A, now the resultant ratio of the milk and water in vessel A is 8: 5, then find the initial quantity of the milk in vessel A?

A) 20 liters

B) 30 liters

C) 40 liters

D) 50 liters

E) None of these

2) Â Ratio of the ages of Minu and Tinu is 3: 2 and the sum of the ages of Binu and Rinu after 8 years is 66 years. If the ratio of the ages of Rinu and Sinu is 2:5 and the ratio of the ages of Binu and Sinu after 10 years is 2: 3. 10 years ago Tinuâ€™s age is equal to the present age of Binu. What is the ratio of the sum of the present ages Minu and Sinu together to average of the present ages of Tinu, Binu and Rinu together?

A) 5: 2

B) 8: 5

C) 11: 3

D) 13: 6

E) None of these

3) Â Ratio of the marked price to cost price of the mobile is 11: 10 and the ratio of the marked price to cost price of the laptop is 23: 20. If the cost price of the mobile is half of the cost price of the laptop and the selling price of the mobile is Rs.9000. If the selling price of the laptop is Rs.14000 more than that of the selling price of the mobile, then what is the discount offered on mobile?

A) Rs.4900

B) Rs.4500

C) Rs.4300

D) Cannot be determined

E) None of these

4) A, B and C started the work together and after two-fifth of the work is complete C left the work. Then A and B continues the work and after 16 days A and B stopped the work, and then C complete the remaining work in 4 days. If C complete 80% of the work in 48 days and the efficiency of B is twice of A, in how many days B alone complete half of the work?

A) 24.5 days

B) 23.5 days

C) 22.5 days

D) 20.5 days

E) None of these

5) A and E together can complete the half of the work in 15 days. B and C together can complete the 75% of the work in 30 days and C and D together can complete the eleven-twelfth of work in 44 days. A, B and E together can complete the half of the work in 10 days.

From the statement given in the above question which of the following can be determined.

A)Â E alone complete half of the work

B)Â B alone complete 75% of the work.

C)Â A and B together can complete 25% of the work

D)Â B and D together can complete the work

A) All A, B, C and D

B) Only B and D

C) All A, B and D

D) Only B

E) Cannot be determine

6) Train A crosses train B running opposite direction in 12 seconds and the ratio of the length of train A to B is 3: 1. Train A crosses platform in 39 seconds and the speed of train A is 60 kmph which is half of the speed of train B.

From the statement given in the above question which of the following can be determined.

A)Â Length of platform A

B)Â Length of train A

C)Â Time taken by train B crosses the pole

D)Â Time taken by train B crosses the tunnel

A) All A, B, C and D

B) Only B and C

C) Only D and B

D) Only A, B and C

E) Only A, B and D

7) Pipe A can fill the 75% of the tank in 9 hours and Pipe B fills half of the tank in 9 hours. Pipe C can fill 45% of the tank in 9 hours. For the first one hour pipe A and B opened, next one hour pipe A and C opened and then next one hour pipe A and B opened and so on. In how many hours the tank fill completely?

A) 5 (1/3) hours

B) 6 (1/3) hours

C) 7 (1/3) hours

D) 8 (1/3) hours

E) None of these

8) Ratio of the area of the rectangle to perimeter of the square is 4: 1 and the ratio of the length to breadth of the rectangle is 2: 1. If the area of the rectangle is equal to the perimeter of the rhombus whose side is 72 cm, then what is the difference between the area of the square and the perimeter of the rectangle?

A) 252

B) 278

C) 284

D) 296

E) None of these

9) The radius of the cone to sphere is 1: 2 and the volume of the cone is 308 cm3. The height of the cone is 6 cm and the ratio of the radius of the sphere to cylinder is 4:1. If the total surface area of the cylinder is 330 cm2, then what is the volume of the cylinder?

A) 432.75 cm3

B) 412.75 cm3

C) 422.75 cm3

D) 442.75 cm3

E) None of these

10) There are 30 balls mixture of red, yellow and blue in the ratio of 2: 3: 1. Box A contains 20% of the red balls, 40% yellow balls and 20% of blue balls and remaining number of red, blue and yellow be box B. What is the difference between the probability of two yellow balls drawn from A and three red balls drawn from B?

A) 397/1140

B) 407/1140

C) 417/1140

D) 427/1140

E) None of these

Directions (1-10) :

(5x + 30) /(3x + 20) = 8/5

24x + 160 = 25x + 150

x = 10

Quantity of the milk = 5 * 10 = 50 liters

M/T = 3/2

B + R = 66 â€“ 16 = 50

R/S = 2/5

(B + 10)/(S + 10) = 2/3

2S + 20 = 3B + 30

2S â€“ 3B = 10 ———(1)

T â€“ 10 = B

B + 2S/5 = 50

5B + 2S = 250 ——-(2)

(2) â€“ (1)

8B = 240

B = 30

T = 30 + 10 = 40

B + R = 50

R = 50 â€“ 30 = 20

2S/5 = 20

S = 50

M = 3/2 * 40 = 60

Required ratio = (60 + 50):(30 + 40 + 20)/3

= 110:30

=11:3

CP of laptop = x

CP of mobile = x/2

SP of mobile = 9000

SP of laptop = 9000 + 14000 = 23000

C = 48 * 100/80 = 60 days

C done the work in 4 days = 4/60 = 1/15

A + B + C together done the work = 2/5

Remaining work = 1 â€“ 1/15 â€“ 2/5 = 8/15

A + B together completes 8/15 of the work in 16 days

A + B complete the whole work = 16/8 * 15 = 30 days

A + B = 1/30

1/2x + 1/x = 1/30

(1 + 2)/2x = 1/30

1/x = 1/45

x = 45 days

B complete the half of the work = 45/2 = 22.5 days

A + E = 1/30

B + C = 100/75 * 30 = 40

C + D = 12/11 * 44 = 48

A + B + E = 1/20

B = 1/20 â€“ 1/30 = 1/60

B alone complete 75% of the work = 3/4 * 60 = 45 days

C = 1/40 â€“ 1/60 = 1/120

D = 1/48 â€“ 1/120 = 72/120 * 48 = 1/80

B + D = 1/60 + 1/80 = 7/240

B + D = 240/7 days

Length of train A = 3x

Length of train B = x

Speed of train A = 60 kmph

Speed of train B = 120 kmph

4x = (60 + 120) * 5/18 * 12

4x = 180 * 5/18 * 12

4x = 600

x = 150 m

Length of train A = 3 * 150 = 450

450 + length of the platform = 60 * 5/18 * 39

450 + length of the platform = 650

Length of the platform = 200

Time taken by train B crosses a pole = (150/120 * 5/18) = 4.5 seconds

A = 100/75 * 9 = 12 hours

B = 2/1 * 9 = 18 hours

C = 100/45 * 9 = 20 hours

LCM of (12, 18 and 20) = 360

Pipe A fill tank in one hour = 30 units

Pipe B fill tank in one hour = 20 units

Pipe C fill tank in one hour = 18 units

A and B together can fill the tank in one hour = 30 + 20 = 50 units

A and C together can fill the tank in one hour = 30 + 18 = 48 units

First two hours total work completed in = 50 + 48 = 98 units

First 6 hours the total work completed in = 98 * 3 = 294

After 7 hours = 294 + 50 = 344

Remaining work done by A and C together in= 16/48 = 1/3 hours

Total time = 7 (1/3) hours

Perimeter of the rhombus = 4a

Side of the rhombus = 72 cm

Perimeter of the rhombus = 72 * 4 = 288

Area of the rectangle = l * b

2x * x = 288

x = 12 cm

Length of the rectangle = 12 * 2 = 24 cm

Breadth of the rectangle = 12 * 1 = 12 cm

Perimeter of the rectangle = 2 (24 + 12) = 72 cm

Perimeter of the square = 1/4 * 288 = 72 cm

Side of the square = 72/4 = 18 cm

Area of the square = 18 * 18 = 324

Difference = 324 â€“ 72 = 252 cm

Volume of the cone = 1/3 * 22/7 * r * r * h

308 = 1/3 * 22/7 * r * r * 6

Radius of the cone = 7 cm

Radius of the sphere = 2/1 * 7 = 14 cm

Radius of the cylinder = Â¼ * 14 = 3.5 cm

TSA of the cylinder = 2 * 22/7 * r * (h + r)

330 = 2 * 22/7 * 3.5 * (3.5 + h)

Height of the cylinder = 11.5 cm

Volume of the cylinder = 22/7 * r * r * h

= 22/7 * 3.5 * 3.5 * 11.5 = 442.75 cm3

Red balls = 2/6 * 30 = 10

Yellow balls = 3/6 * 30 = 15

Blue balls = 1/6 * 30 = 5

Red balls from A = 20/100 * 10 = 2

Yellow balls from A = 40/100 * 15 = 6

Blue balls from A = 20/100 * 5 = 1

Red balls from B = 10 â€“ 2 = 8

Yellow balls from B = 15 â€“ 6 = 9

Blue balls from B = 5 â€“ 1 = 4

2 Yellow balls drawn from A = 6C2/9C2Â = 5/12

Three red balls drawn from B = 8C3/21C3Â = 4/95

Difference = 5/12 – 4/95 = 427/1140

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