Explanation
$${\textbf{Step- 1: Calculating the work they do in 1 day}}$$
$${\text{A does the work in 25 days,}}$$
$$\therefore {\text{ The work A does in 1 day = }}\dfrac{{\text{1}}}{{{\text{25}}}}$$
$${\text{B does the work in 20 days,}}$$
$$\therefore {\text{ The work B does in 1 day = }}\dfrac{{\text{1}}}{{{\text{20}}}}$$
$${\text{A's and B's toghether work in 1 day = }}\dfrac{{\text{1}}}{{{\text{25}}}}{\text{ + }}\dfrac{{\text{1}}}{{{\text{20}}}}{\text{ = }}\dfrac{{\text{9}}}{{{\text{100}}}}$$
$${\textbf{Step- 2: Solving further}}$$
$${\text{A's and B's work toghether in 5 days = 5 }} \times {\text{ }}\dfrac{{\text{9}}}{{{\text{100}}}}{\text{ = }}\dfrac{{{\text{45}}}}{{{\text{100}}}}$$
$${\text{Work remaining after 5 days = 1 - }}\dfrac{{{\text{45}}}}{{{\text{100}}}}{\text{ = }}\dfrac{{{\text{55}}}}{{{\text{100}}}}$$
$${\text{This work is done by B alone,}}$$
$$\therefore {\text{ Time taken = }}\dfrac{{{\text{Work remaining}}}}{{{\text{Work B does in 1 day}}}}$$
$$ \Rightarrow {\text{ Time taken = }}\dfrac{{\dfrac{{{\text{55}}}}{{{\text{100}}}}}}{{\dfrac{{\text{1}}}{{{\text{20}}}}}}{\text{ = 11}}$$
$${\textbf{Hence option B is correct }}$$
From Given data, X's 1 day work $$= \dfrac{1}{8}$$ Y's 1 day work $$ = \dfrac{1}{12}$$ IF X, Y and Z complete the work in $$3$$ days , then Z's $$1 $$ day work = One day work of X, Y and Z combined - ( One day work of X + One day work of )
$$=\dfrac{1}{3} - [ \dfrac{1}{8} + \dfrac{1}{12}]$$
$$ = \dfrac{1}{3} -[\dfrac{3 + 2}{24}]$$
$$ = \dfrac{1}{3} - \dfrac{5}{24} = \dfrac{8-5}{24} = \dfrac{3}{24}$$ Now we have to find Z's share of the salary. X's share: Y's share : Z's share $$= \dfrac{1}{8}: \dfrac{1}{12} : \dfrac{3}{24}: 3:2:3$$ Z share of wage from the total wage of $$Rs 400 = \dfrac{1}{(3+2+3)} \times 400 = Rs 150.$$
$${\textbf{Step - 1: Finding number of work units for the first case}}{\text{.}}$$
$${\text{Total 36 men work for a total of 18 days to complete it}}{\text{.}}$$
$${\text{So total work units}} = 36 \times 18 = 648$$
$${\text{Thus, for the first case ,it's a total of 648 work units}}{\text{.}}$$
$${\textbf{Step - 2: Finding number of days for the second case}}{\text{.}}$$
$${\text{Let it takes }}x{\text{ days for the workers to complete the task,so we can write}}$$
$${\text{Number of work units}} = 27 \times x = 27x$$
$${\text{Also, the work is same so the work units must be same}}$$
$${\text{So, equating the work units for the two cases, we get}}$$
$$648 = 27x$$
$$x = \dfrac{{648}}{{27}} = 24$$
$${\textbf{Hence option D is correct}}$$
In $$21 $$ days $$280$$ m wall build by $$72$$ man
Then in one day $$280$$ m wall build by man =$$21\times 72$$
Or one day one m wall build by man=$$\dfrac{21\times 72}{280}$$
Or one day 100 m wall build by man =$$\dfrac{21\times 72\times 100}{280}$$
Or 18 days 100 m wall build by man=$$\dfrac{21\times 72\times 100}{280\times 18}=30$$ man
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