# SBI PO 2019 Prelims: Quant Test Day 27

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- Question 1 of 10
##### 1. Question

1 pointsCategory: Quantitative Aptitude**In a school there are 950 students, if 60% boys know swimming but total 38% of the students don’t know swimming. Find how many girls know swimming. If number of boys are 230 more than the number of girls.**Correct**Answer-3) 235**

Explanation –

Total boys = 230 + total girls

Total boys + total girls = 950

230 + total girls + Total girls = 950

2 × Total girls = 720

Total girls = 360

Total boys = 590

Total student who know swimming = 62% of 950 = 589

Total boys who know swimming = 60% of 590 = 354

Total girls who know swimming = 589-354 = 235Incorrect**Answer-3) 235**

Explanation –

Total boys = 230 + total girls

Total boys + total girls = 950

230 + total girls + Total girls = 950

2 × Total girls = 720

Total girls = 360

Total boys = 590

Total student who know swimming = 62% of 950 = 589

Total boys who know swimming = 60% of 590 = 354

Total girls who know swimming = 589-354 = 235 - Question 2 of 10
##### 2. Question

1 pointsCategory: Quantitative Aptitude**In a department the no. of males and no. of females are in the ratio of 3:2. If the no. of males are increased by 10% and no. of females are increased by 19, then the new ratio of the no. of males to females is 4:3. What is the total strength of the department after increase?**Correct**Answer -3) 231**

Explanation

Let the no. males initially are 3x

After increase 3.3x

No. of females initially = 2x

After increase = 2x + 19

According to question,

3.3x / 2x + 19 = 4 / 3

x = 40

Strength = 3.3x + 2x + 19 = 5.3x + 19 = 5.3 × 40 +19 = 231Incorrect**Answer -3) 231**

Explanation

Let the no. males initially are 3x

After increase 3.3x

No. of females initially = 2x

After increase = 2x + 19

According to question,

3.3x / 2x + 19 = 4 / 3

x = 40

Strength = 3.3x + 2x + 19 = 5.3x + 19 = 5.3 × 40 +19 = 231 - Question 3 of 10
##### 3. Question

1 pointsCategory: Quantitative Aptitude**Total cost of three gadgets A, B and C is Rs. 7500 and ratio of cost of A to B is 2:3 while the cost of C is Rs. 1100 more than the cost of B. If A is sold at 20% profit and B is sold at 25% loss. At what price C should be sold for overall profit of 20%.**Correct**Answer- 5) Rs. 5280**

Explanation-

Let the cost price of A = 2x

Cost price of B = 3x

Cost price of C 3x + 1100

Total cost = 2x + 3x + 3x + 1100 = 8x+1100

8x +1100 = 7500

x = 800

Cost of A = 1600

Cost of B = 2400

Cost of C = 3500

Profit on selling A = 20% of 1600 = 320

Loss on selling B = 25% 0f 2400 = 600

Required overall profit = 20% of 7500 = 1500

A + B + C = 1500

320 + (-600) + C = 1500

C = 1780

Hence, C should be sold at 3500 + 1780 = 5280Incorrect**Answer- 5) Rs. 5280**

Explanation-

Let the cost price of A = 2x

Cost price of B = 3x

Cost price of C 3x + 1100

Total cost = 2x + 3x + 3x + 1100 = 8x+1100

8x +1100 = 7500

x = 800

Cost of A = 1600

Cost of B = 2400

Cost of C = 3500

Profit on selling A = 20% of 1600 = 320

Loss on selling B = 25% 0f 2400 = 600

Required overall profit = 20% of 7500 = 1500

A + B + C = 1500

320 + (-600) + C = 1500

C = 1780

Hence, C should be sold at 3500 + 1780 = 5280 - Question 4 of 10
##### 4. Question

1 pointsCategory: Quantitative Aptitude**Boat “A” which sails at 9km/hr in still water starts chasing Boat “B”, from 8km behind, another one which sails at 5km/hr in the upstream direction. After how long will it catch up if the stream is flowing at 2km/hr?**Correct**Answer -4) 4hr**

Explanation

Speed of boat A in upstream = 9-2=7

Relative speed of boat A with respect to boat B (in Upstream) = 7-5 = 2km/hr

Distance to cover = 8km/hr

Time taken = 8km/ relative speed = 8/2 = 4hrIncorrect**Answer -4) 4hr**

Explanation

Speed of boat A in upstream = 9-2=7

Relative speed of boat A with respect to boat B (in Upstream) = 7-5 = 2km/hr

Distance to cover = 8km/hr

Time taken = 8km/ relative speed = 8/2 = 4hr - Question 5 of 10
##### 5. Question

1 pointsCategory: Quantitative Aptitude**To reach city B from city A, at 6am, Parag will have to travel at an average speed of 36km/hr. He will reach City B at 5am if he travels at 48km/hr. At what average speed should Parag travel to reach City B at 4am?**Correct**Answer -2) 72km/hr**

Explanation

Let the taken to reach at 4am is t

Time taken to reach at 5am = t+1

Time taken to reach at 6am = t+2

Since distance is constant

36(t+2) = 48(t+1)

t = 2

putting t=2

Distance = 48(2+1) = 48 × 3

Speed = (48 × 3) / 2 = 72km/hrIncorrect**Answer -2) 72km/hr**

Explanation

Let the taken to reach at 4am is t

Time taken to reach at 5am = t+1

Time taken to reach at 6am = t+2

Since distance is constant

36(t+2) = 48(t+1)

t = 2

putting t=2

Distance = 48(2+1) = 48 × 3

Speed = (48 × 3) / 2 = 72km/hr - Question 6 of 10
##### 6. Question

1 pointsCategory: Quantitative Aptitude**Two trains cross each other in 36 seconds when they are moving in opposite direction and when they are moving in the same direction they cross each other in 540 seconds. The speed of slower train is what percent of the speed of faster train?**Correct**Answer -5) 87.5%**

Explanation

Let the speed of slower train is s and speed of faster train is f

Ratio of time = 36 : 540 = 1 : 15

Ratio of their relative speed ,

( f+s) : (f- s) = 15 : 1

f = 8, s = 7

Percent

7 / 8 × 100 = 87.5%Incorrect**Answer -5) 87.5%**

Explanation

Let the speed of slower train is s and speed of faster train is f

Ratio of time = 36 : 540 = 1 : 15

Ratio of their relative speed ,

( f+s) : (f- s) = 15 : 1

f = 8, s = 7

Percent

7 / 8 × 100 = 87.5% - Question 7 of 10
##### 7. Question

1 pointsCategory: Quantitative Aptitude**Ratio of efficiency of A and B in completing a work is 4:3. Both started to work together but B left after 2 days. Another person C joins A and they together completed the remaining work in 7days. If A and B together can complete the work in 12 days, then in how many days C alone can complete the work?**Correct**Answer -5) 14days**

Explanation –

Let the efficiency of A = 4x

Efficiency of B = 3x

Total efficiency of A and B = 7x

Time taken by A and B together to finish the work is 12days

Let total work = (combined efficiency of A and B) × 12 days

Total work = 7x × 12 days = 84x

Work done by A and B in 2 days = 7x × 2 = 14x

Work left = 84x – 14x = 70x

Time × (4x + C) = 70x

7 × (4x + C) = 70x

C = 6x

Time taken by C alone = 84x / 6x = 14daysIncorrect**Answer -5) 14days**

Explanation –

Let the efficiency of A = 4x

Efficiency of B = 3x

Total efficiency of A and B = 7x

Time taken by A and B together to finish the work is 12days

Let total work = (combined efficiency of A and B) × 12 days

Total work = 7x × 12 days = 84x

Work done by A and B in 2 days = 7x × 2 = 14x

Work left = 84x – 14x = 70x

Time × (4x + C) = 70x

7 × (4x + C) = 70x

C = 6x

Time taken by C alone = 84x / 6x = 14days - Question 8 of 10
##### 8. Question

1 pointsCategory: Quantitative Aptitude**There are 7 filling pipes, each capable of filling a cistern alone in 6 minutes and 5 empty pipes each capable of emptying the cistern alone in 8 minutes. All pipes are opened together and as a result tank gets filled by 13 litres of water per minute. Find the capacity of the tank.**Correct**Answer – 2) 24 litres**

Explanation –

Tank filled per minute by filling pipe = 1/6

Tank filled per minute by 7 filling pipe = 7/6

Tank emptied per minute by emptying pipe = 1/8

Tank emptied per minute by 5 emptying pipe = 5/8

When all pipes are opened, tank filled per minute = 7/6 – 5/8

= 13/24

Tank will be fully filled in = 24/13 minutes

Capacity of tank = 24/13 × 13 = 24 litresIncorrect**Answer – 2) 24 litres**

Explanation –

Tank filled per minute by filling pipe = 1/6

Tank filled per minute by 7 filling pipe = 7/6

Tank emptied per minute by emptying pipe = 1/8

Tank emptied per minute by 5 emptying pipe = 5/8

When all pipes are opened, tank filled per minute = 7/6 – 5/8

= 13/24

Tank will be fully filled in = 24/13 minutes

Capacity of tank = 24/13 × 13 = 24 litres - Question 9 of 10
##### 9. Question

1 pointsCategory: Quantitative Aptitude**Two customers are visiting a particular shop in the same week (Monday to Friday). Each is equally likely to visit the shop on any one day as on another. What is the probability that both will visit the shop on different days?**Correct**Answer-2) 4/5**

Explanation-

Total number of days to visit the shop = 5

Total number of possible outcomes = 5 × 5 = 25

Number of favourable outcomes (for visiting the shop on same day) = 5 i.e., (M,M), (Tu,Tu,) (W,W), (Th,Th, ) ( F,F)

Probability (for visiting the shop on same day) = 5/25 = 1/5

Probability (for visiting the shop on different days) = 1 – Probability (for visiting the shop on same day)

Probability (for visiting the shop on different days) = 1 – 1/ 5 = 4/5Incorrect**Answer-2) 4/5**

Explanation-

Total number of days to visit the shop = 5

Total number of possible outcomes = 5 × 5 = 25

Number of favourable outcomes (for visiting the shop on same day) = 5 i.e., (M,M), (Tu,Tu,) (W,W), (Th,Th, ) ( F,F)

Probability (for visiting the shop on same day) = 5/25 = 1/5

Probability (for visiting the shop on different days) = 1 – Probability (for visiting the shop on same day)

Probability (for visiting the shop on different days) = 1 – 1/ 5 = 4/5 - Question 10 of 10
##### 10. Question

1 pointsCategory: Quantitative Aptitude**A glass contains a mixture of apple, sugarcane and orange juices in the respective ratio of 5:6:4. 15ml of this mixture is taken out and 16ml of orange juice and 4ml of sugarcane juice are added to the glass. If the resultant quantity of orange juice is 8ml less than the resultant quantity of sugarcane juice, what was the initial quantity of mixture in the glass?**Correct**Answer- 3) 165ml**

Explanation

After 15ml mixture is taken out,

Let the quantity of apple juice, sugarcane juice and orange juice in the glass is 5x, 6x and 4x respectively.

According to question,

(6x + 4) – (4x +16) = 8ml

x = 10

15x = 150

Adding 15ml which was taken in the beginning,

150+15 = 165mlIncorrect**Answer- 3) 165ml**

Explanation

After 15ml mixture is taken out,

Let the quantity of apple juice, sugarcane juice and orange juice in the glass is 5x, 6x and 4x respectively.

According to question,

(6x + 4) – (4x +16) = 8ml

x = 10

15x = 150

Adding 15ml which was taken in the beginning,

150+15 = 165ml

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