Question

ayan working for 2 days and sayan working for 3 days complete 3/5 of a work. Again ayan working for 3 days and sayan working for 4 days complete 13/15 of the work. how many more days sayan will taken then ayan to complete the work, if they work separately..? ​

Answer 1

Answer:

form equation and adding each other we get x and y values

Answer 2

Answer:

10 days

Step-by-step explanation:

Let Ayan completes a job in x days

Let Sayan completes a job in y days

Ayan working for 2 days and Sayan working for 3 days to complete 3/5 of a work.

Ayan do work in 2 days $=\dfrac{2}{x}$

Sayan do work in 3 days $=\dfrac{3}{y}$

Both completes 3/5 of works.

$\dfrac{2}{x}+\dfrac{3}{y}=\dfrac{3}{5}-------------(1)$

Again ayan working for 3 days and Sayan working for 4 days complete 13/15 of the work.

Ayan do work in 3 days $=\dfrac{3}{x}$

Sayan do work in 4 days $=\dfrac{4}{y}$

Both completes 13/15 of works.

$\dfrac{3}{x}+\dfrac{4}{y}=\dfrac{13}{15}-----------(2)$

Now, solve system of equation.

Multiply first equation by 3 and second equation by -2

$\dfrac{6}{x}+\dfrac{9}{y}=\dfrac{9}{5}$

$-\dfrac{6}{x}-\dfrac{8}{y}=-\dfrac{26}{15}$

Add both equation

     $\dfrac{1}{y}=\dfrac{27-26}{15}=\dfrac{1}{15}$

                   $y=15$

Put y=15 into first equation

$\dfrac{2}{x}+\dfrac{3}{15}=\dfrac{3}{5}$

                   $x=5$

Ayan completes job in 5 days.

Sayan completes job in 15 days.

Difference = 15 - 5

                 = 10

Hence, Sayan takes 10 days more than Ayan