Question

sanju can do a piece of work in 4 days and sumit can do it 6days. how long will they take if both sanju and sumit work together.

Answer 1

Let total amount of the work be 'z',
amount of work which Sanju can do in a day be 'x' and amount of work which Sumit can do in a day be 'y'.

As per the question, Sanju can do a piece of work in 4 days>>4x=z____(1)
Also,it is given that Sumit takes 6days for same work >>6y=z____(2)

From(1),x=z/4
From(2),y=z/6

When both of them work together,
Number of days=Total work/amount of work they can do in a day
=z/(x+y)
$= \frac{z}{ \frac{z}{4} + \frac{z}{6} }$
=z/(10z/24)
=24/10=2.4days

Thus, they take 2.4days(2days and 9.6hours)to complete the work

Hope this helps you

Answer 2

$\frac{1}{4} + \frac{1}{6} = \frac{3 + 2}{12} \\ = \frac{5}{12 } \\ this \: clculation \: is \: done \: in \: efficiency \\ to \: convertdays \: take \: reciprocl \\ \frac{12}{5} days \\ \: 2 \frac{2}{5} days$