To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?

(a) 30 days

(b) 35 days

(c) 40 days

(d) 45 days

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Solution

Let B can do a work in =x days

Then A can do the work

$= x + \frac{x}{2} = \frac{3}{2} x$ days

A and B 1 days work $= \frac{1}{18}$

A's 1 day's work $= \frac{1}{x}$

and B's 1 day's work $= \frac{2}{3 x}$

$∴ \frac{1}{x} + \frac{2}{3 x} = \frac{1}{18}$

$\frac{5}{3 x} = \frac{1}{18} \Rightarrow 3 x = 5 \times 18$

$\Rightarrow x = \frac{5 \times 18}{3} = 30$

$∴$ B can do the work in =30 days

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To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it? (a) 30 days (b) 35 days (c) 40 days (d) 45 days

Let B can do a work in =x days Then A can do the work =x+x2=32x days A and B 1 days work =118 A's 1 day's work =1x and B's 1 day's work =23x ∴1x+23x=118 53x=118⇒3x=5×18 ⇒x=5×183=30 ∴ B can do the work in =30 days

To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?

(a) 30 days

(b) 35 days

(c) 40 days

(d) 45 days