SBI Clerk Mains Quantitative Aptitude (Day-18)

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Application Sums

1) Two trains are moving in opposite direction on parallel tracks. Speed of the trains is in the ratio of 3: 4. Also the time taken by the trains to cross a man in 5 sec and 10 sec respectively.

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

A) Length ratio of the trains

B) Time taken to cross each other

C) Length of the trains

a) Only A

b) Both A & C

c) Both A & B

d) All

e) None

2) A swimmer swims 48 km upstream and 56 km downstream in 12 hrs. Also, he can swim 54 km upstream and 70 km downstream in 14 hrs.

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

A) Distance covered by the swimmer in 10 hrs upstream

B) Speed of the swimmer in still water

C) Downstream speed

a) Only C

b) Only C & A

c) Only C & B

d) All

e) None

3) Pipe A can fill a tank fully in 20 min and pipe B can empty the tank completely in 15 min. Tank is filled up to X%, then both pipes are opened and the tank is emptied in 18 min. What is the value X?

a) 11%

b) 30%

c) 19%

d) 13%

e) None of these

4) A and B enter into a business with the investment ratio of 1: 2 respectively. After 4 months B withdraws and C joins with x amount. A receives Rs.390 out of the total profit Rs.950. What is the value of x?

a) Rs.260

b) Rs.170

c) Rs.150

d) Rs.300

e) None of these

5) A person reduced his consumption by 25% since the price increased by 20%. Expenditure comes down by 10% and if the expenditure after price increase is Rs.81, find the initial expenditure.

a) Rs.90

b) Rs.10

c) Rs.99

d) Rs.99

e) None of these

Data Interpretation

Direction (6 – 10): Study the following data carefully and answer the questions?

In a factory, labour productivity is calculated on yearly basis. There are total two types of productivity: Labour productivity per hour and Labour productivity per worker. Formula to calculate labour productivity is given below:

Labour productivity per hour = Worth of Output produced/Total hours input

Labour productivity per worker = Worth of Output produced/Total workers input

Also, there is one more term called efficiency to calculate the efficiency of the workforce of the company. Formula to calculate efficiency is given below:

Efficiency = (Standard Labour Hours/Amount of Time Worked) * 100

Table given below shows the Standard Labour hours and total number of workers allotted for the work on five different years in the company:

 

6) If in 2011, efficiency of the workforce of the company is 66(2/3)% and Labour productivity per hour is Rs.105/hour, then what is the total worth of the output produced by the company in 2011?

a) Rs.12600

b) Rs.13200

c) Rs.11400

d) Rs.10800

e) None of these

7) If labour productivity per worker and efficiency of the company in 2012 is Rs.175/worker and 120% respectively, then what is the labour productivity per hour of the company in 2012?

a) 190

b) 225

c) 185

d) 210

e) None of these

8) If labour productivity per hour and labour productivity per worker of the company in 2013 is Rs.90/hour and Rs.180/worker, then what is the efficiency of company in 2013?

a) 80%

b) 125%

c) 120%

d) 75%

e) None of these

9) If efficiency of the company in 2014 is 125% and labour productivity per hour of the company in 2014 is Rs.75/hour, then what is the labour productivity per worker (of the company in 2014?

a) 125.5

b) 112.5

c) 87.5

d) 145.5

e) None of these

10) If efficiency of the company in 2015 is 62.5% and total worth of output produced by the company in 2015 is Rs.18600, then what is the difference between labour productivity per hour and labour productivity per worker of the company in 2015?

a) 205

b) 125

c) 155

d) 145

e) None of these

Answers :

Directions (1-5) :

1) Answer: C

l1 = 3x * 5, l2 = 4x * 10

l1: l2 = 15: 40 = 3: 8

15x + 40x = (3x + 4x) * t

= > t = 55/7 s

From the statement, we can find the ratio of length of the trains and time taken to cross each other.

2) Answer: D

48/Us + 56/Ds = 12

54/Us + 70/Ds = 14

Substituting 1/Us = u, 1/Ds = d

48u + 56d = 12 —— 1

54u + 70d = 14 —— 2

Solving 1 & 2, u = 1/6, v = 1/14

Us = 6 kmph, Ds = 14 kmph

From the statement, we can find all the above.

3) Answer: B

1/20 – 1/15 = -1/60

Full tank can be emptied in 60 min

X = 100 * 18/60 = 30%

4) Answer: C

A: B: C = (y * 12): (2y * 4): (x * 8) = 3y: 2y: 2x

3y = 390 = > y = 130

2y = 130 * 2 = 260

2x = 950 – (390 + 260) = 300

= > x = Rs.150

5) Answer: A

Expenditure = Price * Quantity

New expenditure = 120/100 * 75/100 = 9/10

9/10 = > 81

Initial expenditure = 81/9 * 10 = Rs.90

Directions (6-10) :

6) Answer: A

Efficiency = (80/Amount of time worked) * 100

66(2/3) = (80/Amount of time worked) * 100

2/3 = 80/Amount of time worked

Amount of time worked = 120 hours

Labour productivity per hour = Worth of Output produced/Total hours input

105 = Worth of Output produced/120

Worth of Output produced = 105 * 120 = Rs.12600

7) Answer: D

Labour productivity per worker = Worth of Output produced/Total workers input

175 = Worth of output produced/60

Worth of output produced = 175 * 60 = Rs.10500

Efficiency = (Standard Labour Hours/Amount of Time Worked) * 100

120 = (60/Amount of time worked) * 100

6/5 = (60/Amount of time worked) * 100

Amount of time worked = 50 hours

Labour productivity per hour = Worth of Output produced/Total hours input

= 10500/50 = 210

8) Answer: C

Labour productivity per worker = Worth of Output produced/Total workers input

180 = Worth of Output produced/50

Worth of Output produced = 180 * 50 = Rs.9000

Labour productivity per hour = Worth of Output produced/Total hours input

90 = 9000/Total hours input

Total hours input = 9000/90 = 100 hours

Required efficiency = (120/100) * 100 = 120%

9) Answer: B

Efficiency = (Standard Labour Hours/Amount of Time Worked) * 100

125 = (150/Amount of Time Worked) * 100

Amount of Time Worked = (150 * 100)/125 = 120 hours

Labour productivity per hour = Worth of Output produced/Total hours input

75 = Worth of Output produced/120

Worth of Output produced = 75 * 120 = Rs.9000

Labour productivity per worker = Worth of Output produced/Total workers input

= 9000/80

= Rs.112.5 per worker

10) Answer: C

Efficiency = (Standard Labour Hours/Amount of Time Worked) * 100

62.5 = (125/Amount of Time Worked) * 100

Amount of Time Worked = (125 * 100)/62.5 = 200 hours

Total worth of output produced by the company in 2015 = Rs.18600

Labour productivity per hour = Worth of Output produced/Total hours input

= 18600/200 = Rs.93/hour

Labour productivity per worker = Worth of Output produced/Total workers input

= 18600/75 = Rs.248/worker

Required difference = 248 – 93 = Rs.155

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