X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work?
A. $$13\frac{1}{3}$$ days
B. 15 days
C. 20 days
D. 26 days
Answer: Option A
Solution(By Examveda Team)
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
$$\eqalign{ & = {\frac{{{\text{40}}}}{{\text{3}}}} \cr & {\text{ = 13}}\frac{{\text{1}}}{{\text{3}}}\,\,{\text{days}} \cr} $$
Join The Discussion
Comments ( 2 )
Related Questions on Time and Work
A. 18 days
B. 24 days
C. 30 days
D. 40 days
Assume total work as 100units ,
And divide 100 by 40 to get the efficience of X, then u will get 2.5 units of efficiency per day.
Then later multiply 2.5 with 8 to get total work done by X , then we get 20.
20 units is the work done done by X.
Deduct 20 from 100 to know remaining work
100 - 20 = 80.
So 80 units of work is remaining.
Divide 80 by 16 to know Y's efficiency.
80/16 = 5.
So combined efficiency of X and Y is
2.5 + 5 = 7.5
So finally..
Divide 100 by 7.5
100/7.5 =13.33
That is 13⅓ days
Can you pl provide any shortcut method for this sum for reducing time...?