Question

4 Indians and 4 Chinese can do a piece of work in 3 days while 2 Indians and 5 Chinese can finish it in 4 days. How long would it take for 1 Indian to do it ? How long would it take for 1 Chinese to do it?

Answer 1

Answer:

1 Indian can do the work in 18 days while 1 Chinese can do the work in 36 days

Step-by-step explanation:

Let 1 Indian can do the work in x days and 1 Chinese can do the work in y days

Indian can do in in 1 day = 1/x work

Chinese can do in 1 day = 1/y work

Indian and Chinese together can do in 1 day = 1/x + 1/y work

4 Indian and 4 Chinese together can do in 1 day = 4/x + 4/y) work

4 Indian and 4 Chinese together can do in 3 day = 3(4/x + 4/y) work

According to the question

$12(\frac{1}{x}+\frac{1}{y})=1$

$\implies \frac{1}{x}+\frac{1}{y}=\frac{1}{12}$   .........(1)

2 Indian and 5 Chinese together can do in 1 day = (2/x + 5/y) work

2 Indian and 5 Chinese together can do in 4 day = 4(2/x + 5/y) work

According to the question

$4(\frac{2}{x}+\frac{5}{y})=1$

$\implies \frac{2}{x}+\frac{5}{y}=\frac{1}{4}$   .........(2)

Multiplying eq (1) by 2 and subtracting it from eq (1)

$\frac{5-2}{y}=\frac{1}{4}-\frac{2}{12}$

$\implies \frac{3}{y}=\frac{3-2}{12}$

$\implies \frac{3}{y}=\frac{1}{12}$

$\implies y=12\times3$

$\implies y=36$

Putting the value of y in eq (1)

$\frac{1}{x}+\frac{1}{36}=\frac{1}{12}$

$\implies \frac{1}{x}=\frac{1}{12}-\frac{1}{36}$

$\implies \frac{1}{x}=\frac{3-1}{36}$

$\implies \frac{1}{x}=\frac{2}{36}$

$\implies x=18$

Therefore, 1 Indian can do the work in 18 days while 1 Chinese can do the work in 36 days