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__START QUIZ__

1)

**The ratio of time taken by a boat to cover (x + 4) km in upstream to that of time taken to cover (x + 20) km in still water is 4: 5. If the ratio of speed of boat in downstream to that of stream is 5: 1 and the sum of time taken by the boat to cover (x – 5) km in upstream to that in downstream is 8 hours then find the speed of boat in downstream?**
a) 1 km/hr

b) 3 km/hr

c) 4 km/hr

d) 5 km/hr

e) 8 km/hr

2)

**There are 5 red bikes, “x” blue bikes and “y” black bikes in a showroom. The probability that a blue bike is selected for test drive is 7/24 while the probability that a black bike is selected for test drive is ½. Find the value of (x – y + x * y).**
a) 81

b) 79

c) 82

d) 78

e) 83

3)

**There are two containers P and Q. P contains 56 kg of salt and Q contains 36 kg of sugar. From P 24 kg of salt is taken out and poured into Q. Then 20kg of the mixture from Q is taken out and poured into P. Find the ratio of final quantity of salt to sugar in container P.**
a) 10/3

b) 20/3

c) 5/3

d) 2/3

e) 40/3

4)

**A train X running at the speed of 126 km/hr crosses a man running at 18 km/hr in opposite direction in 12 seconds and crosses a platform ‘’A’’ in 20 seconds. Find the time taken by train Y running at 99 km/hr to cross the platform ‘’B’’. The length of the platform ‘’B’’ is 70 m more than the length of the platform “A” and the length of train Y is equal to the length of train “X”.**
a) 24 seconds

b) 28 seconds

c) 36 seconds

d) 32 seconds

e) 22 seconds

5)

**A, B, and C together can complete a piece of work in 25 days. A and C together can complete 30% of the work in 12 days and B and C together can complete 75% of the work in 33 days. A is 50% more efficient than C. In how many days (approximate integer value) B alone can complete the whole work?**
a) 72 days

b) 75 days

c) 79 days

d) 85 days

e) 82 days

**Directions (6-10) :**

There are 3 types of departments namely Electrical, Electronics and Telecommunication in a company and certain number of people were working in all three departments. Each person was working on one department or the other. 64% people where in Electrical department. People working in Telecommunication department only were 1/16 of the Electrical department. Person working in both Electronics and Telecommunication department except Electrical department were 55. Person working in only Electronics department is equal to person in Telecommunication department only + 29.

**6.What is the total number of people working in Electronics department only?**

1. 41

2. 38

3. 36

4. 51

5. 31

7.

**What is the total number of people working in the company?**
1. 200

2. 300

3. 400

4. 500

5. 600

8.

**What is the difference between the number of people working in both Electronics and Telecommunication department except Electrical department to the sum of the number of people working in Telecommunication department only and Electronics department only?**
1. 7

2. 6

3. 5

4. 2

5. 1

9.

**What is the total number of people working in Electrical department?**
1. 180

2. 128

3. 256

4. 320

5. 192

10.

**If 50 people are working in both electrical and telecommunication except electronics department and 22 people are working in both electrical and electronics department except telecommunication department, then find the number of people working in electrical department only if no one is working in all three departments?**
1. 110

2. 120

3. 105

4. 90

5. 130

__SOLUTIONS:__**1) Answer: d)**

**Let the downstream speed be 5p and speed of stream be p**

**Then speed of boat in still water will be 5p – p = 4p**

**And speed of boat in upstream will be 4p – p = 3p**

**Time taken to cover (x + 4) km in upstream = (x + 4)/3p**

**And time taken to cover (x + 20) km in still water = (x + 20)/4p**

**{(x + 4)/3p}: {(x + 20)/4p} = 4: 5**

**{(x + 4)}/{(3x + 60)} = 1/5**

**5x + 20 = 3x + 60**

**x = 20**

**Also,**

**The sum of time taken by the boat to cover (x – 5) km in upstream to that in downstream is 8 hours.**

**(x – 5) = 20 – 5 = 15 km**

**15/3p + 15/5p = 8**

**5/p + 3/p = 8**

**8/p = 8**

**p = 1 km/hr**

**The speed of boat in downstream = 5p = 5 * 1 = 5 km/hr**

**2) Answer: b)**

**ATQ,**

**Probability of a blue bike is selected for test drive = x/(5 + x + y) = 7/24**

**24x = 35 + 7x + 7y**

**17x – 7y = 35 (equation 1)**

**Also,**

**Probability that a black bike is selected for test drive = y/(5 + x + y) = ½**

**2y = 5 + x + y**

**x = y – 5**

**Putting x = y – 5 in equation 1**

**17(y – 5) – 7y = 35**

**17y – 85 – 7y = 35**

**10y = 120**

**y = 12 and x = 12 – 5 = 7**

**(x – y + x * y) = 7 – 12 + 7 * 12 = – 5 + 84 = 79**

**3) Answer: a)**

**Initially, the Amount of sugar in Q = 36kg**

**Now, 24kg of salt is poured in Q,**

**Total quantity in Q becomes = 36kg (sugar) + 24kg (salt) = 60kg (mixture)**

**The ratio of salt to sugar in Q becomes = 24: 36 = 2: 3**

**Again, 20kg of the mixture is taken out from Q and poured into P**

**Therefore, quantity of salt and sugar in P becomes**

**= {(56 – 24) + 20 * (2/5)} kg of salt + 20 * (3/5) kg of sugar**

**= (32 + 8) kg of salt + 12 kg of sugar**

**= 40 kg of salt + 12 kg of sugar**

**Required ratio = (40/12) = (10/3)**

**4) Answer: b)**

**Let the length of train X = x meter**

**Relative speed of train and man when running in opposite direction = 126 + 18**

**= 144km/hr = 144 * (5/18) = 40 m/s**

**ATQ,**

**40 = x/12**

**x = 480 m**

**Let the length of the platform “A” = P1**

**126 * (5/18) = (P1 + 480)/20**

**35 = (P1 + 480)/20**

**P1 + 480 = 700**

**P1 = 220m**

**The length of platform “B” = P2 = 220 + 70 = 290**

**Speed of train Y = 99 km/hr = 99 * (5/18) = 27.5 m/s**

**Time taken by train Y to cross the platform B = (480 + 290)/27.5**

**= (770)/27.5 = 28 seconds**

**5) Answer: c)**

**Therefore, work of A, B, and C together in one day = 1/25**

**A and C together can complete 30% of the work in 12 days**

**100% work will be done in (2/5)*100 = 40 days**

**Work by A and C together in one day = 1/40**

**Since A is 50% more efficient than C**

**Let per day work done by C = x and per day work done by A will be = 150% of x = (150/100)*x = 1.5x**

**x + 1.5x = 1/40**

**2.5x = 1/40**

**x = 1/100**

**Therefore per day one done by C = 1/100 and**

**Per day work done by A = 1.5*(1/100) = 1.5/100 = 3/200**

**Also,**

**B and C together can complete 75% of the work in 33 days**

**100% work will be completed in (33/75)*100 = 44 days**

**Work done by B and C in one day = 1/44**

**Let the one day work done by B = x**

**Therefore,**

**x + 1/100 = 1/44**

**x = 1/44 – 1/100**

**x = 7/550**

**Therefore, days taken by B alone to complete the work = 550/7 = 78.57 (79 approx)**

**6.**

**Answer-1) 41**

**Explanation:**

**People working in Electronics department only = 4x + 29 =12+29 =41**

**Complete Explanation –**

**Let Electrical is denoted as El, electronics only as Et and Telecommunications only is denoted as T**

**Let the no. of people working in the company = 100x**

**People working in Electrical department = 64% of 100x = 64x**

**People working in Telecommunication department only = 1/16 * 64x = 4x**

**People working in both Electronics and Telecommunication department except Electrical department = 55**

**People working in Electronics department only = 4x +29**

**SBI PO Main Quant test day 1 Q(6-10)**

**Total = 100x**

**100x = 64x +4x+29 +55 + 4x**

**28x = 84**

**x = 3**

**Therefore total people = 100x = 100*3 = 300**

**People working in Electrical department = 64x = 64*3 = 192**

**People working in Telecommunication department only = 1/16 * 64x = 4x = 4*3 = 12**

**People working in Electronics department only = 4x + 29 =12+29 =41**

**7.**

**Answer- 2) 300**

**Explanation**

**Let the no. of people working in the company = 100x**

**100x = 64x +4x+29 +55 + 4x**

**28x = 84**

**x = 3**

**8.**

**Answer- 4) 2**

**Explanation**

**55 – (41+12) = 2**

**9.**

**Answer- 5) 192**

**Explanation-**

**People working in Electrical department = 64% of 100x = 64x = 64*3 = 192**

**10.**

**Answer- 2) 120**

**Explanation–**

**192 – (50+22) = 120**