Question

A,B and C working together can finish a work in 3 days. A can do it alone in 6 days and B can do it in 7 1/2 days. In how many days can C alone finish the same work?in detail​

Answer 1

Answer:

3 members together finishes work = 3 days

3 members together finishes work in 1 day = $\dfrac{1}{3}$

A finishes work = 6 days

A finishes work in 1 day = $\dfrac{1}{6}$

B finishes work = 7 $\dfrac{1}{2}$ days

B finishes work= $\dfrac{15}{2}$

B finishes work in 1 day = $\dfrac{1}{\dfrac{15}{2}}$

B finishes work in 1 day =$1\times \dfrac{2}{15}$

B finishes work in 1 day = $\dfrac{2}{15}$

C finishes work in 1 day = $\dfrac{1}{3} - [\dfrac{1}{6}+\dfrac{2}{15}]</p><p>[tex] \leadsto \dfrac{1}{3} - [\dfrac{5+2}{30}]$

$\leadsto \dfrac{1}{3} - [\dfrac{7}{30}]$

$\leadsto \dfrac{1}{3} - \dfrac{7}{30}$

$\leadsto \dfrac{10-7}{30}$

$\leadsto\dfrac{3}{30}$

$\leadsto\dfrac{\cancel{3}}{\cancel{30}}$

$\leadsto\dfrac{1}{10}$

Therefore C finishes work in 10 days

Answer 2

Answer:

When they work together the rate at which they complete the work will add up, that is the portion of work completed in a single day.

For A, the rate is 1/2, for B it is 1/3 and for C it is 1/6

Their cumulative rate is 1/2 + 1/3 + 1/6 = (1/6)(3+2+1) = 1, which means they will complete the entire portion of the work in a day.