51
A is thrice as good a workman as B. C alone takes 48 days to paint a house. All three A, B and C working together take 16 days to paint the house. It will take how many days for B alone to paint the house?
Answer & Solution
Answer: Option
C
Solution:
A = 3B
\[\therefore \frac{{\text{A}}}{{\text{B}}} = \frac{3}{1}\begin{array}{*{20}{c}} { \times 2} \\ { \times 2} \end{array}\]
\[\frac{{\text{C}}}{{{\text{A}} + {\text{B}} + {\text{C}}}} = \frac{1}{3}\begin{array}{*{20}{c}} { \times 4} \\ { \times 4} \end{array}\]
Efficiency :- A + B + C
\[\begin{array}{*{20}{c}} {\text{A}}&{\text{B}}&{\text{C}} \\ {}&{12}&6 \\ 2&4&{} \end{array}\]
∵ A + B + C do work in 16 days
Total work = 12 × 16
∴ B will do work in $$ = \frac{{12 \times 16}}{2} = 96{\text{ days}}$$
\[\therefore \frac{{\text{A}}}{{\text{B}}} = \frac{3}{1}\begin{array}{*{20}{c}} { \times 2} \\ { \times 2} \end{array}\]
\[\frac{{\text{C}}}{{{\text{A}} + {\text{B}} + {\text{C}}}} = \frac{1}{3}\begin{array}{*{20}{c}} { \times 4} \\ { \times 4} \end{array}\]
Efficiency :- A + B + C
\[\begin{array}{*{20}{c}} {\text{A}}&{\text{B}}&{\text{C}} \\ {}&{12}&6 \\ 2&4&{} \end{array}\]
∵ A + B + C do work in 16 days
Total work = 12 × 16
∴ B will do work in $$ = \frac{{12 \times 16}}{2} = 96{\text{ days}}$$
