Two farm workers Mutua and Musyoka can cultivate a field in 6 days. Mutua alone can complete the cultivation in 15 days. After Mutua and Musyoka had worked for 4 days, Mutua fell sick

Two farm workers Mutua and Musyoka can cultivate a field in 6 days. Mutua alone can complete the cultivation in 15 days. After Mutua and Musyoka had worked for 4 days, Mutua fell sick. Find the time taken by Musyoka to complete the cultivation.

Answers

Let Musyoka take x days

In 1 day Mutua cultivates

$\frac{1}{15}$

In 1 day Musyoka cultivates

$\frac{1}{x}$

In 1 day both had done

$\frac{1}{6}$ x 4 =

$\frac{2}{3}$

Fraction of work remaining is

1 -

$\frac{2}{3}$ =

$\frac{1}{3}$

To complete the work

$\frac{1}{15}$ +

$\frac{1}{x}$ =

$\frac{1}{6}$ ;

$\frac{1}{x}$ =

$\frac{1}{6}$ -

$\frac{1}{15}$ ;

$\frac{1}{x}$ =

$\frac{1}{10}$

x = 10 days: Musyoka alone would take 10 days to complete the work.

To complete the remaining

$\frac{1}{3}$

Musyoka would take

$\frac{1}{10}x$ =

$\frac{1}{3}$ ; x =

$\frac{10}{3}$ = 3

$\frac{1}{3}$ days

johnmulu answered the question on March 6, 2017 at 06:32

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