Question

8 girls and 12 boys can finish work in 10 days while 6 girls and 8 boys can finish it in 14 days. Frame linear equations for calculating the time taken by the one girl alone( x) that by one boy alone (y) to finish the work.​

Answer 1

Answer:

Step-by-step explanation:

Let boys be termed as y

Let girls be termed as x

So,

According to the question,

10*(8x + 12y) = Work Done = 14*(6x + 8y)

So, let's simplify it,

80x + 120y = 84x + 112y

120y - 112y = 84x - 80x

8y = 4x

y = 1/2x      (i.e., work done by 1 boy is equal to the work done by 1/2 girl)

x = 2y        (i.e., work done by 1 girl is equal to the work done by 2 boys)

So, we can say that,

if x = 2y,

then,

8x = 16y

=> 16y + 12y = 28y (28 boys are required to work for 10 days to do full work)

So, if 10 days are required by 28 boys to do a work,

then,

28*10 boys are required to do the work in 1 day

So, if 280 boys = 1 day

then, 1 boy = 280 days

∴ Time required by 1 boy to do the work = 280 days

And we know that 1 girl = 2 boys,

So, we can safely say that the time required by 1 girl to do the work will be half of what will be required by 1 boy.

So, days required by 1 girl to do the work = 280/2 = 140 days.