Question

has written.
Both of Lalima and Romen clean their garden. If Lalima works for 4 days and Romen
works for 3 days, then part of the work is completed. Again, if Lalima works for 3 days
and Romen works for 6 days, then part of the work is completed. Let us form the
Simultaneous equations and write the number of days required to complete the work
separately by Lalima and Romen by calculating the solution.​

Answer 1

Given :

To complete a part of work

The number of days did Lalima worked = 4

The number of days did Romen worked = 3

Again

To complete a part of work

The number of days did Lalima worked = 3

The number of days did Romen worked = 6

To Find :

The number of days did Lalima worked alone = x days

The number of days did Romen worked alone = y days

Solution :

Lalima's 1 day work = $\dfrac{1}{x}$

So, Lalima's 4 day work = $\dfrac{1}{x}$ × 4 = $\dfrac{4}{x}$

Romen's 1 day work = $\dfrac{1}{y}$

So, Romen's 3 day work = $\dfrac{1}{y}$ × 3 = $\dfrac{3}{y}$

∴ 1 day work for Lalima and Romen = $\dfrac{4}{x}$  + $\dfrac{3}{y}$  = 1

or,  $\dfrac{4}{x}$  + $\dfrac{3}{y}$  = 1

or,  4 y + 3 x = x y                ...........1

Again

Lalima's 3 day work = $\dfrac{1}{x}$ × 3 = $\dfrac{3}{x}$

Romen's 6 day work = $\dfrac{1}{y}$ × 6 = $\dfrac{6}{y}$

∴ 1 day work for Lalima and Romen  working together = $\dfrac{3}{x}$  + $\dfrac{6}{y}$  = 1

or,   $\dfrac{3}{x}$  + $\dfrac{6}{y}$  = 1  = 1

or, 3 y + 6 x = x y                ...........2

Solving eq 1 and 2

2 (  4 y + 3 x ) - ( 3 y + 6 x ) = 2 × x y - x y

Or,  ( 8 y - 3 y ) + ( 6 x - 6 x ) = x y

Or,   5 y + 0 = x y

∴     x = 5

So, Number of days did Lalima work alone is 5 days

Put The value of x into eq 2

3 y + 6 x = x y    

Or,  3 y + 6 × 5 = 5 y

Or,  5 y - 3 y = 30

Or,           2 y = 30

∴                 y = $\dfrac{30}{2}$

i.e               y = 15 days

So, Number of days did Romen work alone is 15 days

Hence,.

Number of days did Lalima work alone is 5 days

Number of days did Romen work alone is 15 days

Answer

Answer 2

no.of day lalima work 5 days

no.of day Roman work 15 days