A boat is moving upstream on a river. It has a speed of x km/hr. in still water. The river is flowing at a speed of 3 km/h * r . a) What will be the speed of the boat as it goes upstream? b) Similarly, what will be the speed of the boat as it goes downstream? c) What will be the distance covered by the boat (upstream) in 3 hours? d) What is likely to happen if the speed of the boat is equal to the speed of the river, as it goes upstream?
Answers
Answer:
Let speed of the boat in still water =xkm/hr and speed of the stream =ykm/hr
Then, the speed of the boat downstream =(x+y)km/hr And speed of the boat upstream =(x−y)km/hr
According to the question
Condition I:
When boat goes 16km upstream, let the time taken be
t
1
. Then,
t
1
=
x−y
16
h[∵time=
speed
distance
]
When boat goes 24km downstream, let the time taken be t
2
.
Then, t
2
=
x+y
24
h
But total time taken (t
1
+t
2
)=6 hours
∴
x−y
16
+
x+y
24
=6…(a)
Condition II:
When boat goes 12km upstream, let the time taken be T
1
Then, T
1
=
x−y
12
h[∵ time =
speed
distance
]
When boat goes 36km downstream, let the time taken be T
2
. Then,
T
2
=
x+y
36
h
But total time taken (T
1
+T
2
)=6 hours
∴
x−y
12
+
x+y
36
=6…(b)
Now, we solve tis pair of linear equations by elimination method
x+y
16
+
x−y
24
=6…(i)
And
x+y
12
+
x−y
36
=6…(ii)
On multiplying Eq. (i) by 3 and Eq. (ii) by 4 to make the coefficients equal of first term, we get the equation as
x+y
48
+
x−y
72
=18…(iii)
x+y
48
+
x−y
144
=24…(iv)
On substracting Eq. (iii) from Eq. (iv), we get
⇒
x+y
16
+
12
24
=6
⇒
x+y
16
=6−2
⇒
x+y
16
=4
⇒x+y=4…(b)
Adding Eq. (a) and (b), we get ⇒2x=16
⇒x=8
On putting value of x=8 in eq. (a), we get 8−y=12
⇒y=−4 but speed can't be negative ⇒y=4
Hence, x=8 and y=4, which is the required solution.
Hence, the speed of the boat in still water is 8km/hr and speed of the stream is 4km/hr
Step-by-step explanation:
Step-by-step explanation:
While British traders in seventeenth-century South Asia were largely based in the coastal areas and rarely engaged in local politics, by the middle of the eighteenth century their attitude had changed significantly. Clashes with the Mughal Emperor and his provincial deputies concluded with the surrender of Bengal, the richest province of the empire, to Company control. Following three successful wars against their chief European competitor, the French Compagnie des Indes Orientales, the British had gained a greater stronghold in the south and soon a Company political representative or ‘Resident’ was sent to every significant court in the subcontinent. Here they exerted considerable influence and control, pulling strings to ensure that local ministers contracted treaties favourable to the Company.
As the East India Company’s power and confidence grew, many rulers of the subcontinent reached out to successive British monarchs, entreating them to intervene in the actions of their subjects, the Company servants. Letters and gifts, including manuscripts and paintings, were sent between South Asia and Britain, and relationships developed between the House of Hanover and many of India’s ruling dynasties. East India Company officers also presented gifts to British monarchs, and by the end of the eighteenth century the Royal Library had amassed one of the most splendid collections of South Asian paintings and manuscripts outside the subcontinent.