Question

(i) Sunil takes 5 days more than Anil to complete a certain work. 4 days after starting
the work, Anil left the work. The remaining work was done by Sunil in 5 days.
Find how many days each will take to complete the work.​

Answer 1

Answer:

Anil takes 10 days and Sunil takes 15 days

Step-by-step explanation:

Let the number of days Anil needed to complete the work be x

⇒ 1 day = 1/x

Sunil takes 5 days more than Anil to complete the work

⇒ Number of days = x + 5

⇒ 1 day = 1/(x + 5)

Find the amount of work they did in 4 days:

1 day = 1/x + 1/(x + 5)

1 day = (x + 5 + x)/x(x+ 5)

1 day = (2x + 5)/x(x+ 5)

4 days = 4(2x + 5)/x(x+ 5)

Find the amount of work Sunil did in 5 days:

1 day = 1/x + 5)

5 days = 5/(x + 5)

Solve x:

4(2x + 5)/x(x+ 5) + 5/(x + 5) = 1

4(2x + 5) + 5x = x(x + 5)

8x + 20 + 5x = x² + 5x

x² - 8x - 20 = 0

(x - 10)(x + 2) = 0

x = 10 or x = -2 (Negative, rejected)

Find the number of days each take:

Anil = x = 10 days

Sunil = x + 5 = 10 + 5 = 15 days

Answer: Anil takes 10 days and Sunil takes 15 days