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?

#### Solution

Let the time taken by a Indian be “x”

Time taken by a Chinese be “y”

Work done by a Indian in one day = `1/x`

Work done by a Chinese in one day = `1/y`

By the given first condition

(4 Indian + 4 Chinese) finish the work in 3 days

`4/x + 4/y = 1/3` → (1)

Again by the given second condition

(2 Indian + 5 Chinese) finish the work in 4 days

`2/x + 5/y = 1/4` → (2)

Solve the equation (1) and (2)

Let `1/x` = a, `1/y` = b

4a + 4b = `1/3`

12a + 12b = 1 → (3) ...(Multiply by 3)

2a + 5b = `1/4`

8a + 20b = 1 → (4) ...(Multiply by 4)

(3) × (2) ⇒ 24a + 24b = 2 → (5)

(4) × (3) ⇒ 24a + 60b = 3 → (6)

(5) – (6) ⇒ −36b = −1

b = `1/36`

Substitute the value of b = `1/36` in (3)

`12"a" + 12(1/36)` = 1

`12"a" + 1/3` = 1

36a + 1 = 3

36a = 2

a = `2/36 = 1/18`

But `1/x` = a ⇒ `1/x = 1/18`

x = 18

`1/y` = b ⇒ `1/y = 1/36`

y = 36

∴ Time taken by a 1 Indian is 18 days

Time taken by a 1 Chinese is 36 days