Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 9th

# 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 - Mathematics

Sum

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

Concept: Consistency and Inconsistency of Linear Equations in Two Variables
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