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**Directions (1 â€“ 5): The following questions are accompanied by three statements I, II and III. You have to determine which statement is/are sufficient to answer the questions. **

**1) A and B together can complete the work in how many days?**

I) A alone can complete the work in 12 days.

II) B alone can complete the work in 18 days.

III) A and B together can complete (5/6)^{th} of the work in 6 days.

a) Both I and II alone are sufficient

b) If Either III alone or both I and II are sufficient

c) Either I or III are sufficient

d) Both I and III are sufficient

e) All three are sufficient

**2) Find the perimeter of square, whose side is 4 meter less than the length of the rectangle?**

I) The ratio between the length to that of breadth of the rectangle is 3: 2.

II) The perimeter of the rectangle is 80 meter.

III) The area of the rectangle is 384 Sq meter.

a) Both I and II are sufficient

b) Both I and III are sufficient

c) Any two of the given statement are sufficient

d) All three statements are sufficient

e) Either I and II or I and III are sufficient

**3) Find the present age of Sanu?**

I) 5 years ago, the ratio of age of Kathir and Sanu is 3: 2.

II) After 7 years, the ratio of age of Kathir and Sanu will be 21: 16.

III) The difference between the age of Kathir and Sanu is 10 years.

a) Both I and II are sufficient

b) Both I and III are sufficient

c) All three statements are sufficient

d) Any two of the given statement are sufficient

e) Either I and II or I and III are sufficient

**4) Find the speed of train B (in km/hr)?**

I) Train A crosses 150 m long train B running in opposite directions in 18 sec.

II) The speed of train A is 50 km/hr.

III) The length of train A is twice that of train B

a) Both I and II alone are sufficient

b) If Either III alone or both I and II are sufficient

c) Either I or III are sufficient

d) Any two of the given statement are sufficient

e) All three are sufficient

**5) What is speed of the boat in still water?**

I) The boat takes 6 hours to travel 48 km downstream

II) The boat takes 2 hours more to travel same distance upstream.

III) The ratio of speed of boat in still water to that of stream is 7: 1.

a) Either I and II or I and III are sufficient

b) Both I and II are sufficient

c) Both II and III are sufficient

d) All three statements are sufficient

e) Both I and III are sufficient

**Directions (6 â€“ 10): The two-line graph shows the distance travelled by the five different boats with the stream and against the stream in same time and the bar chart shows speed of stream.Â Â Â Â Â Â Â **

**6) Find out the speed of Boat B & D together in still water is approximately how much percentage more/less than that of speed of stream of the same boats together?**

a) 70 %

b) 170%

c) 60%

d) 68%

e) 150%

**7) It is known that ratio of the speed of the Boat B to Boat F in the still water is 4:5. If itâ€™s given that Boat F travels 126 km distance with the stream, and 81 km against the stream in 7 hr 30 min, what is the speed of stream for Boat F?**

a) 14

b) 13

c) 15

d) 12

e) 18

**8) Itâ€™s known that distance between the two-point M & N is 210 km. Boat E travels from point M to N and Comes back. What is the time taken by Boat E in travelling total distance?**

a) 12

b) 14

c) 18

d) 17

e) 16

**9) Captain of the Boat thought of increasing the speed of Boat C and so in still water speed of boat is increased by 10% and stream also started flowing fast, increasing its speed by 20% due to wind. Find the time taken by the Boat C to cover 91km distance against the stream.**

a) 7

b) 8.5

c) 3.5

d) 6.2

e) None of these

**10)** **Find the ratio of the speed of Boats A and B together in still water to the speed of Boats D and E together in still water.**

a) 48:55

b) 48:65

c) 43:33

d) 46:34

e) 44:34

**Answers :**

**Direction (1-5) :**

**1) Answer: b)**

**From I and II,**

Aâ€™s one day work = 1/12

Bâ€™s one day work = 1/18

(A + B)â€™s one day work = (1/12) + (1/18) = 30/(12*18) = 5/36

(A + B)â€™s one day work = 36/5 = 7 (1/5) days

Both I and II are sufficient to answer the question.

**From III,**

A and B together can complete (5/6)^{th} of the work = 6 days

(5/6)*Work = 6

(A + B) can complete the work in, 6*(6/5) = 36/5 = 7 (1/5) days

Statement III alone are sufficient to answer the question.

**So, Either III alone or both I and II are sufficient**

**2) Answer: c)**

**From I and II, **

The ratio between the length to that of breadth of the rectangle = 3: 2 (3x, 2x)

The perimeter of the rectangle = 80 meter

2*(3x + 2x) = 80

5x = 40

X = 8

Length = 3x = 24 m

Side of square (a) = 20 m

Perimeter of square = 4a = 80 m

Both I and II are sufficient to answer the question.

**From I and III, **

The ratio between the length to that of breadth of the rectangle = 3: 2 (3x, 2x)

The area of the rectangle = 384 Sq meter

3x*2x = 384

6x^{2} = 384

X^{2} = 384/6 = 64

X = 8

Length = 3x = 24 m

Side of square (a) = 20 m

Perimeter of square = 4a = 80 m

Both I and III are sufficient to answer the question.

**From II and III,**

The perimeter of the rectangle = 80 meter

2*(l + b) = 80

= > l+ b = 40

= > b = 40 – l

The area of the rectangle = 384 Sq meter

= > lb = 384

= > l*(40 â€“ l) = 384

40l â€“ l^{2} = 384

L^{2} â€“ 40l + 384 = 0

(l – 24) (l â€“ 16) = 0

L = 24, 16

If l = 24, then b = 40 â€“ 24 = 16

If l = 16, then b = 40 â€“ 16 = 24

The length of rectangle is always greater than breadth. So,

L = 24, b = 16

Side of square (a) = 20 m

Perimeter of square = 4a = 80 m

Both II and III are sufficient to answer the question.

**Hence, any of the three statements are necessary to answer the given question.**

**3) Answer: d)**

**From I and II, **

(3x + 12) / (2x + 12) = 21/16

48x + 192 = 42x + 252

6x = 60

= > x = 10

Present age of Sanu = 2x + 5 = 25 years

Both I and II are sufficient to answer the question.

**From I and III, **

5 years ago, Kathir: Sanu = 3: 2

3x â€“ 2x = 10

= > x = 10

Present age of Sanu = 2x + 5 = 25 years

Both I and III are sufficient to answer the question.

**From II and III, **

After 7 years, Kathir: Sanu = 21: 16

21x â€“ 16x = 10

5x = 10

= > x = 2

Present age of Sanu = 16x â€“ 7 = 32 â€“ 7 = 25 years

Both II and III are sufficient to answer the question.

**Hence, any of the three statements are necessary to answer the given question.**

**4) Answer: e)**

**From I, II and III,**

Length of train A = 2*150 = 300 m

According to the question,

(300 + 150)/[(50 + x)*(5/18)] = 18

(450*18)/[(50 + x)*5] = 18

90 = 50 + x

X = 40 Km/hr

**Hence, all three statements are required to answer the question.**

**5) Answer: a)**

**From I and II, **

Speed of downstream = 48/6 = 8 km/hr

Speed of upstream = 48/8 = 6 km/hr

Speed of boat in still water = (1/2)*14 = 7 km/hr

Both I and II are sufficient to answer the question.

**From I and III, **

Speed of downstream = 48/6 = 8 km/hr

8x = 8

X = 1

Speed of boat in still water = 7x = 7 km/hr

Both I and III are sufficient to answer the question.

**Hence, either I and II or I and III are sufficient to answer the given questions.**

**Directions (6 – 10): **

**Boat A: **

Let us take speed of boat A in still water be x kmph

Given,

288/(x+12) = 96/(x-12)

3/(x+12) = 1/(x-12)

3x-36 = x+12

2x = 48 => x= 24 kmph

Speed of boat A in still water is 24 kmph

**Boat B: **

Let us take speed of boat B in still water be x kmph

Given,

240/(x+8) = 120/(x-8)

2/(x+8) = 1/(x-8)

X+8 = 2x-16=> x= 24 kmph

Speed of boat B in still water is 24 kmph

**Boat C: **

Let us take speed of boat C in still water be x kmph

Given,

220/(x+15) = 100/(x-15)

11/(x+15) = 5/(x-15)

11x-165 = 5x+75

6x = 240 => x= 40 kmph

Speed of boat C in still water is 40 kmph

**Boat D: **

Let us take speed of boat D in still water be x kmph

Given,

350/(x+10) = 150/(x-10)

7/(x+10) = 3/(x-10)

7x-70 = 3x+30

4x = 100 => x= 25 kmph

Speed of boat C in still water is 25 kmph

**Boat E: **

Let us take speed of boat E in still water be x kmph

Given,

540/(x+20) = 180/(x-20)

3/(x+20) = 1/(x-20)

3x-60 = x+20

2x = 80 => x= 40 kmph

**6) Answer: b)**

Speed of Boat B and D, in still water together = (24 + 25) = 49 km/h

Speed of stream of Boat B and D together = 18 km/h

**7) Answer: d)**

2 (3780 â€“ 126x + 2430 + 81x) = 15 (900 â€“ x^{2})

2 (6210Â â€“ 45x) = 13500Â â€“ 15x^{2}

12420Â â€“ 90x = 13500Â â€“ 15x^{2}

15x^{2}Â â€“ 90xÂ â€“ 1080 = 0

x^{2}Â â€“ 6xÂ â€“ 72 = 0

x^{2}Â â€“ 12x + 6x â€“ 72 = 0

x (xÂ â€“ 12) + 6 (xÂ â€“ 12) = 0

(x + 6) (xÂ â€“ 12) = 0

x =Â â€“6, 12

Speed of stream = 12 km/h

**8) Answer: b)**

**9) Answer: c)**

Speed of Boat C in still water = 40Â Ã— 110% = 44 km/h

Speed of stream = 15Â Ã— 120% = 18 km/h

Time taken by Boat C to cover the distance of 91 km upstream = 91/ (44Â â€“ 18)

= 91/ 26 = 3.5 hours

**10) Answer: b)**

Ratio = (24 + 24) : (25 + 40)

=Â 48 : 65