Direction: Study the data carefully and answer the question given beside:
 
The table shows the distance travelled by five different boats upstream and downstream in same time and the line chart shows the speed of stream

 Boat   Distance (Upstream)    Distance (Downstream) 
P 96 288
Q 120 240
R 100 220
S 150 350
T 180 540

Important for :
1
Find the ratio of the speed of Boats P and Q together in still water to the speed of Boats S and T together in still water.
» Explain it
E
Ratio = (24 + 24) : (25 + 40)

= 48 : 65

Hence, option E is correct.

Common Explanation:

Speed of Boat P in still water = a km/h

96  =  288
(a – 12) (a + 12)

96 (a + 12) = 288 (a – 12)

96a + 1152 = 288a – 3456

3456 + 1152 = 288a – 96a

a = 24 km/h

Speed of Boat Q in still water = b km/h
120  =  240
(b – 8) (b + 8)

120 (b + 8) = 240 (b – 8)

120b + 960 = 240b – 1920

1920 + 960 = 240b – 120b

b = 24 km/h

Speed of Boat R in still water = c km/h
 
100  =  220
(c – 15) (c + 15)

100 (c + 15) = 220 (c – 15)

100c + 1500 = 220c – 3300

3300 + 1500 = 220c – 100c

c = 40 km/h

Speed of Boat S in still water = d km/h
 
150  =  350
(d – 10) (d + 10)

150 (d + 10) = 350 (d – 10)

150d + 1500 = 350d – 3500

3500 + 1500 = 350d – 150d

d = 25 km/h

Speed of Boat T in still water = e km/h
 
180  =  540
(e – 20) (e + 20)

180 (e + 20) = 540 (e – 20)

180e + 3600 = 540e – 10800

10800 + 3600 = 540e – 180e

e = 40 km/h
 
2
If the speed of Boat R in still water is increased by 10% and the speed of stream is increased by 20%, Find the time taken by Boat R to cover the distance of 91 km upstream.
» Explain it
A
Speed of Boat R in still water = 40 × 110% = 44 km/h

Speed of stream = 15 × 120% = 18 km/h

Time taken by Boat R to cover the distance of 91 km upstream = 91/ (44 – 18)

= 91/ 26 = 3.5 hours

Hence, option A is correct.
 
Common Explanation:

Speed of Boat P in still water = a km/h

96  =  288
(a – 12) (a + 12)

96 (a + 12) = 288 (a – 12)

96a + 1152 = 288a – 3456

3456 + 1152 = 288a – 96a

a = 24 km/h

Speed of Boat Q in still water = b km/h
120  =  240
(b – 8) (b + 8)

120 (b + 8) = 240 (b – 8)

120b + 960 = 240b – 1920

1920 + 960 = 240b – 120b

b = 24 km/h

Speed of Boat R in still water = c km/h
100  =  220
(c – 15) (c + 15)

100 (c + 15) = 220 (c – 15)

100c + 1500 = 220c – 3300

3300 + 1500 = 220c – 100c

c = 40 km/h

Speed of Boat S in still water = d km/h
 
150  =  350
(d – 10) (d + 10)

150 (d + 10) = 350 (d – 10)

150d + 1500 = 350d – 3500

3500 + 1500 = 350d – 150d

d = 25 km/h

Speed of Boat T in still water = e km/h
180  =  540
(e – 20) (e + 20)

180 (e + 20) = 540 (e – 20)

180e + 3600 = 540e – 10800

10800 + 3600 = 540e – 180e

e = 40 km/h
 
3
The distance between point A and point B is 210 km. Boat T travels from point A to B and comes back. What is the time taken by Boat T to cover the total distance.
» Explain it
C
Total time =   210  +  210
(40 – 20) (40 + 20)

=   210  +  210
20 60

= 10.5 + 3.5 = 14 hours

Hence, option C is correct.
 
Common Explanation:

Speed of Boat P in still water = a km/h

96  =  288
(a – 12) (a + 12)

96 (a + 12) = 288 (a – 12)

96a + 1152 = 288a – 3456

3456 + 1152 = 288a – 96a

a = 24 km/h

Speed of Boat Q in still water = b km/h
120  =  240
(b – 8) (b + 8)

120 (b + 8) = 240 (b – 8)

120b + 960 = 240b – 1920

1920 + 960 = 240b – 120b

b = 24 km/h

Speed of Boat R in still water = c km/h
 
100  =  220
(c – 15) (c + 15)

100 (c + 15) = 220 (c – 15)

100c + 1500 = 220c – 3300

3300 + 1500 = 220c – 100c

c = 40 km/h

Speed of Boat S in still water = d km/h
 
150  =  350
(d – 10) (d + 10)

150 (d + 10) = 350 (d – 10)

150d + 1500 = 350d – 3500

3500 + 1500 = 350d – 150d

d = 25 km/h

Speed of Boat T in still water = e km/h
 
180  =  540
(e – 20) (e + 20)

180 (e + 20) = 540 (e – 20)

180e + 3600 = 540e – 10800

10800 + 3600 = 540e – 180e

e = 40 km/h
 
4
The ratio of the speeds of the Boat Q to the Boat U in still water is 4 : 5. If the Boat U travels 126 km distance downstream and 81 km distance upstream in 7 hours 30 minutes, What is the speed of stream of Boat U?
» Explain it
D
Speed of the Boat Q in still water = 24 km/h

Speed of the Boat U in still water =  24  × 5 = 30 km/h
4

Let the speed of stream = x km/h

According to the question,
 
126  +  81 = 15
(30 + x) (30 – x) 2

126 (30 – x) + 81 (30 + x)  =  15
(900 – x2) 2

2 (3780 – 126x + 2430 + 81x) = 15 (900 – x2)

2 (6210 – 45x) = 13500 – 15x2

12420 – 90x = 13500 – 15x2

15x2 – 90x – 1080 = 0

x2 – 6x – 72 = 0

x2 – 12x + 6x – 72 = 0

x (x – 12) + 6 (x – 12) = 0

(x + 6) (x – 12) = 0

x = –6, 12

Speed of stream = 12 km/h

Hence, option D is correct.

Common Explanation:

Speed of Boat P in still water = a km/h
96  =  288
(a – 12) (a + 12)

96 (a + 12) = 288 (a – 12)

96a + 1152 = 288a – 3456

3456 + 1152 = 288a – 96a

a = 24 km/h

Speed of Boat Q in still water = b km/h

120  =  240
(b – 8) (b + 8)

120 (b + 8) = 240 (b – 8)

120b + 960 = 240b – 1920

1920 + 960 = 240b – 120b

b = 24 km/h

Speed of Boat R in still water = c km/h

 
100  =  220
(c – 15) (c + 15)

100 (c + 15) = 220 (c – 15)

100c + 1500 = 220c – 3300

3300 + 1500 = 220c – 100c

c = 40 km/h

Speed of Boat S in still water = d km/h

 
150  =  350
(d – 10) (d + 10)

150 (d + 10) = 350 (d – 10)

150d + 1500 = 350d – 3500

3500 + 1500 = 350d – 150d

d = 25 km/h

Speed of Boat T in still water = e km/h

 
180  =  540
(e – 20) (e + 20)

180 (e + 20) = 540 (e – 20)

180e + 3600 = 540e – 10800

10800 + 3600 = 540e – 180e

e = 40 km/h
 
5
The speed of Boat Q and S in still water together is approximately how much percentage more than the speed of stream of the same boats together?
» Explain it
C
According to the question,

Speed of Boat Q and S in still water together = (25 + 24) = 49 km/h

Speed of stream of Boat Q and S together = 18 km/h

% more =  49 – 18  × 100
18

31  × 100 = 172.22% ≈ 170%
18

Hence, option C is correct.

Common Explanation:

Speed of Boat P in still water = a km/h
96  =  288
(a – 12) (a + 12)

96 (a + 12) = 288 (a – 12)

96a + 1152 = 288a – 3456

3456 + 1152 = 288a – 96a

a = 24 km/h

Speed of Boat Q in still water = b km/h

120  =  240
(b – 8) (b + 8)

120 (b + 8) = 240 (b – 8)

120b + 960 = 240b – 1920

1920 + 960 = 240b – 120b

b = 24 km/h

Speed of Boat R in still water = c km/h

 
100  =  220
(c – 15) (c + 15)

100 (c + 15) = 220 (c – 15)

100c + 1500 = 220c – 3300

3300 + 1500 = 220c – 100c

c = 40 km/h

Speed of Boat S in still water = d km/h

 
150  =  350
(d – 10) (d + 10)

150 (d + 10) = 350 (d – 10)

150d + 1500 = 350d – 3500

3500 + 1500 = 350d – 150d

d = 25 km/h

Speed of Boat T in still water = e km/h

 
180  =  540
(e – 20) (e + 20)

180 (e + 20) = 540 (e – 20)

180e + 3600 = 540e – 10800

10800 + 3600 = 540e – 180e

e = 40 km/h
 

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