Question

Formulate the following problems as a pair of equation, hence find their solution:

1. 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.

2. Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60km 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. ( CBSE Xth class chapter : Linear pair equation in two variables)

Answer 1

i)Let time taken by 1 woman alone to finish the work = x days

Let time taken by 1 man alone to finish the work = y days

So, 1 woman’s 1-day work = ()th part of the work

And, 1 man’s 1-day work = ()th part of the work

So, 2 women’s 1-day work = ()th part of the work

And, 5 men’s 1-day work = ()th part of the work

Therefore, 2 women and 5 men’s 1-day work = (+)th part of the work… (1)

It is given that 2 women and 5 men complete work in = 4 days

It means that in 1 day, they will be completing th part of the work … (2)

Clearly, we can see that (1) = (2)

⇒  … (3)

Similarly,  … (4)

Let 

Putting this in (3) and (4), we get

2p + 5q =  and 3p + 6q = 

⇒ 8p + 20q = 1 … (5) and 9p + 18q = 1 … (6)

Multiplying (5) by 9 and (6) by 8, we get

72p + 180q = 9 … (7)

72p + 144q = 8 … (8)

Subtracting (8) from (7), we get

36q = 1⇒ q = 

Putting this in (6), we get

9p + 18 () = 1

⇒ 9p = ½⇒ p = 

Putting values of p and q in , we get x = 18 and y = 36

Therefore, 1 woman completes work in = 18 days

And, 1 man completes work in = 36 days

(iii) Let speed of train = x km/h and let speed of bus = y km/h

According to given conditions,

Let 

Putting this in the above equations, we get

60p + 240q = 4 … (1)

And 100p + 200q =  … (2)

Multiplying (1) by 5 and (2) by 3, we get

300p + 1200q = 20 … (3)

300p + 600q =  … (4)

Subtracting (4) from (3), we get

600q = 20 − = 7.5

⇒ q = 

Putting value of q in (2), we get

100p + 200 () = 

⇒ 100p + 2.5 = 

⇒ 100p = – 2.5

⇒ p = 

But 

Therefore, x =km/h and y = km/h

Therefore, speed of train = 60 km/h

And, speed of bus = 80 km/h