a) $$13\frac{1}{3}$$ days
b) 15 days
c) 20 days
d) 26 days
Answer: a
Explanation: Work done by X in 8 days = $$ {\frac{1}{{40}} \times 8} $$ = $$\frac{1}{5}$$
Remaining work = $$ {1 – \frac{1}{5}} $$ = $$\frac{4}{5}$$
Now, $$\frac{4}{5}$$ work is done by Y in 16 days
Whole work will be done by Y in = $$ {16 \times \frac{5}{4}} $$ = 20 days
X’s 1 day’s work = $$\frac{1}{{40}}$$
Y’s 1 day’s work = $$\frac{1}{{20}}$$
(X + Y)’s 1 day’s work
$$\eqalign{
& = {\frac{1}{{40}} + \frac{1}{{20}}} \cr
& = \frac{3}{{40}} \cr} $$
Hence, X and Y will together complete the work in
$$\eqalign{
& = {\frac{{{\text{40}}}}{{\text{3}}}} \cr
& {\text{ = 13}}\frac{{\text{1}}}{{\text{3}}}\,\,{\text{days}} \cr} $$
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