# SBI Clerk Mains Quantitative Aptitude (Day-11)

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Application Sums

1) Ratio of the speed of the train A to train B is 6: 5 and the ratio of the length of train A to train B is 4: 5. Both trains running in same direction and train A crosses train B in 81 seconds. If the speed of train A is 60 kmph, what is the length of train A?

a) 120 m

b) 150 m

c) 180 m

d) Cannot be determine

e) None of these

2) If the length of the rectangle is increased by 12 cm and the breadth of the rectangle decreased by 6 cm, then the area of the rectangle becomes 168 cm2. When the breadth of the rectangle increased by 4 cm is equal to the original length of the rectangle, what is the original perimeter of the rectangle?

a) 48 cm

b) 56 cm

c) 52 cm

d) 42 cm

e) None of these

3) Vessel A has 40 liters mixture of milk and water in the ratio is 4:1 and the vessel B contains 20 liter mixture of milk and water in the ratio of 3: 1. 10 liters of mixture from vessel A is taken out and poured into vessel B. Then 10 liters of mixture from vessel B taken out and poured into vessel A. What is the percentage of water in the final mixture that the vessel A has?

a) 18(5/6)%

b) 19(5/6)%

c) 20(5/6)%

d) 21(5/6)%

e) None of these

4) A, B and C started the business. A and B invests in the ratio of 3: 2 and the B and C invests in the ratio of 3: 4. At the end of one year the profit received by A is Rs.2400 less than that the profit received by B and B gets 30% of the total profit for managing the business. What is the total profit amount?

a) Rs.11500

b) Rs.12400

c) Rs.13600

d) Rs.15200

e) None of these

5) A shopkeeper marked up the price of mobile by 50% and sold at      (x – 10) % discount and sold the laptop at 10% profit. If the cost price of laptop and mobile is Rs. 120x and Rs. 4800 and the ratio of the profit earned from laptop to mobile is 2: 1.

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

a) Value of x

b) Selling price of laptop

c) Marked price of laptop

d) Ratio of cost price of laptop to mobile

a) A and B

b) All A, B, C and D

c) A, C and D

d) A, B and D

e) A, B and C

Data Interpretation

Direction (6 – 10): Read the following information carefully and answer the given questions?

There are 500 students in a school. Every student likes different color like red, yellow and blue. 36% of the students like Yellow and the ratio of the number of students like red and yellow only to the number of students like yellow and blue only is 2: 3. Number of students like all the colors is 20. Ratio of the number of students like only red to the number of students like only yellow is 3:2. Number of students like yellow only is equal to the number of students like yellow and blue only. Number of students like both red and blue is 50% of the number of students like only blue. The number of students like only Blue is equal to the number of students does not like any color.

6) Find the number of students does not like yellow?

a) 280

b) 300

c) 320

d) 270

e) None of these

7) What is the ratio of the number of students like at most two colors to the number of students like only red, only yellow and only blue together?

a) 32: 23

b) 37: 24

c) 41: 26

d) 48: 25

e) None of these

8) The number of students like Blue is approximately what percent of the number of students like red?

a) 108%

b) 113%

c) 117%

d) 121%

e) 103%

9) What is the difference between the number of students like two colors only and the number of students like at least two colors?

a) 10

b) 15

c) 20

d) 25

e) None of these

10) What is the sum of the number of students does not like any color and the number of students like all the three colors?

a) 100

b) 110

c) 105

d) 115

e) None of these

Directions (1-5) :

Speed of train A = 60 kmph

Speed of train B = 5/6 * 60 = 50 kmph

Length of train A = 4x

Length of train B = 5x

9x = (60 – 50) * 5/18 * 81

9x = 25 * 9

x = 25

Length of train A = 4 * 25 = 100 m

Length of the rectangle = l

Breadth of the rectangle = b

Area of the rectangle = l * b

(l + 12) (b – 6) = 168

b + 4 = l

l – b = 4

(l + 12) (l – 4 – 6) = 168

(l + 12) (l – 10) = 168

l2 – 10l + 12l – 120 = 168

l2 +2l – 288 = 0

(l – 16) (l + 18) = 0

l = 16, -18 (negative value neglect)

Length of the rectangle = 16 cm

Breadth of the rectangle = 16 – 4 = 12 cm

Perimeter of the rectangle = 2 * (l + b)

= 2 * (12 + 16) = 56 cm

Milk in vessel A = 40 * 4/5 = 32

Water in vessel A = 1/5 * 40 = 8

Milk in vessel B = 3/4 * 20 = 15

Water in vessel B = 1/4 * 20 = 5

Milk in 10 liters of the mixture = 4/5 * 10 = 8

Water in 10 liters of mixture = 1/5 * 10 = 2

Now milk vessel A = 32 – 8 = 24 liters

Now water in vessel A = 8 – 2 = 6 liters

Now Milk in vessel B = 15 + 8 = 23

Now Water in vessel B = 5 + 2 = 7

Again 10 liters mixture taken out from vessel B

Milk in 10 liters of mixture = 23/30 * 10 = 23/3

Water in 10 liters of mixture = 7/30 * 10 = 7/3

Now water in vessel A = 6 + 7/3 = 25/3

Now milk in vessel A = 24 + 23/3 = 95/3

Total quantity in vessel A = (25 + 95)/3 = 120/3 = 40

Required percentage = [(25/3) / 40] * 100 = 2500/120

= 125/6 = 20(5/6) %

Profit ratio of A, B and C = 9: 6: 8

Let the total profit = x

B’s management amount = x * 30/100 = 3x/10

Remaining profit = 7x/10

Total profit received by A = 7x/10 * 9/23 = 63x/230

Profit received by B = 6/23 * 7x/10 = 42x/230

Total profit received by B = 3x/10 + 42x/230 = 111x/230

Difference = 111x/230 – 63x/230 = 48x/230

48x/230 = 2400

x = 11500

Cost price of mobile = Rs.4800

Cost price of laptop = 120x

MP of mobile = 150/100 * 4800 = 7200

SP of mobile = 7200 * (100 – x + 10)/100 = 72 * (110 – x)

= 7920 – 72x

Profit of mobile = 7920 – 72x – 4800 = 3120 – 72x

Profit of laptop = 120x * 10/100 = 12x

12x/(3120 – 72x) = 2/1

6x = 3120 – 72x

78x = 3120

x = 40

Cost price of laptop = 120 * 40 = 4800

Selling price of laptop = 4800 * 110/100 = Rs.5280

Ratio = 4800: 4800 = 1: 1

We cannot find the marked price of the laptop.

Directions  (6 – 10):

Total number of students = 500

Number of students like yellow = 36/100 * 500 = 180

Number of students like all the colors = 20

Number of students like only blue = x

Number of students like blue and red = x * 50/100 = x/2

Number of students like red and yellow only = 2y

Number of students like yellow and blue =3y

Number of students like only yellow =3y

Number of students like only red =3/2 * 3y = 9y/2

2y + 20 + 3y + 3y = 180

y = 20

Number of students like red and yellow only = 2y = 40

Number of students like yellow and blue =3y = 60

Number of students like only yellow = 3y = 60

Number of students like only red = 3/2 * 3y = 9y/2 = 90

40 + 60 + 60 + 90 + x + x/2 + x + 20 – 20 = 500

2.5x = 250

x = 100

Number of students like blue and red = 100/2 = 50

Number of students like blue and red only = 50 – 20 = 30 Total number of students = 500

Number of students like yellow = 180

Number of students does not like yellow = 500 – 180 = 320

Number of students like at most two colors

= 90 + 60 + 100 + 30 + 40 + 60 + 100 = 480

Number of students like only red = 90

Number of students like only yellow = 60

Number of students like only blue = 100

Sum = 90 + 60 + 100 = 250

Required ratio = 480: 250

= 48: 25

Number of students like blue =100 + 60 + 30 + 20 = 210

Number of students like red = 90 + 40 + 20 + 30 = 180

Required percentage = 210/180 * 100 = 116.67%

Number of students like only two colors = 40 + 60 + 30 = 130

Number of students like at least two color = 40 + 30 + 20 + 60 = 150

Difference = 150 – 130 = 20