Geography, asked by anshramteke07, 1 month ago

x+y x-y
2(3x + y) 2(3x - y)
8
2. Formulate the following problems as a pair of equations, and hence find their solutions:
() Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her
speed of rowing in still water and the speed of the current.
(ii) 2 women and 5 men can together finish an embroidery work in 4 days, while 3
women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to
finish the work, and also that taken by 1 man alone.
(iii) Roohi travels 300 km to her home partly by train and partly by bus. She takes 4
hours if she travels 60 km by train and the remaining by bus. If she travels 100 km
by train and the remaining by bus, she takes 10 minutes longer. Find the speed of
the train and the bus separately.
My

Answers

Answered by pawarsarita696
0

Answer:

Let, speed of Ritu in still water be x km/hr

and speed of current be y km/hr

Then speed downstream =(x+y) km/hr

speed upstream =(x−y) km/hr

we know, Time=

Speed

Distance

Then x+yy2=2 and

x−y4 =2

⇒x+y=10 ...(1)

& x−y=2 ...(2)

adding both we get, 2x=12⇒x=6

Thus using (1) y=10−6=4

Hence the speed of Ritu in still water is 6 km/hr and the speed of the current is 4 km/hr.

Let the work done by man and woman per day be x and y respectively.

When the work is completed in 4 days

Since 5 men and 2 women complete the work in 4 days

therefore work done by 5 men and 2 women in 1 day =

4

1

∴5x+2y=

4

1

⟶eq

n

1

When the work is completed in 3 days

Since 6 men and 3 women complete the work in 3 days

therefore work done by 6 men and 3 women in 1 day =

3

1

∴6x+3y=

3

1

⟶eq

n

2

Multiplying by 3 in eq

n

1, we get

⇒15x+6y=

4

3

⟶eq

n

3

Multiplying by 2 in eq

n

2, we get

⇒12x+6y=

3

2

⟶eq

n

4

On subtracting eq

n

4 from eq

n

3, we get

⇒15x+6y−12x−6y=

4

3

3

2

⇒3x=

12

1

⇒x=

36

1

On substituting the value of x in eq

n

2, we get

⇒6×

36

1

+3y=

3

1

⇒3y=

3

1

6

1

⇒y=

18

1

Thus,

work done by 1 man in 1 day =

36

1

days

∴ Time taken by 1 man alone to finish the work =36 days

work done by 1 woman in 1 day =

18

1

days

∴ Time taken by 1 woman alone to finish the work =18 days

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