Question

A and B can finish a work in 18 days but time taken by A if he works alone is 18+p and B working alone take 18+ q days also p:q=9:4 what will be the efficiency of A and B

Answer 1

Answer:

A alone can finish a work in 45 days

B alone can finish a work in 30 days

Step-by-step explanation:

Given:

A can finish a work = (18+p) days

B can finish a work = (18+q) days

$\implies$

A's 1 day work $=\frac{1}{18+p}$

B's 1 day work $=\frac{1}{18+q}$

(A+B)'s 1 day work $=\frac{1}{18+p}+\frac{1}{18+q}$

But, as per given data,

(A+B)'s 1 day work $=\frac{1}{18}$

$\mplies\:\frac{1}{18+p}+\frac{1}{18+q}=\frac{1}{18}$

$\mplies\:\frac{18+q+18+p}{(18+p)(18+q)}=\frac{1}{18}$

$\mplies\:\frac{36+p+q}{(18+p)(18+q)}=\frac{1}{18}$

$\mplies\:18(36+p+q)=(18+p)(18+q)$

$\mplies\:36(18)+(p+q)18=18^2+(p+q)18+pq$

$\mplies\:36(18)=18^2+pq$

$\mplies\:18(18)=pq$

$\mplies\:324=pq$

$\mplies\:q=\frac{324}{p}$.........(1)

Also, p:q = 9:4

$\frac{p}{q}=\frac{9}{4}$

$4p=9(\frac{324}{p})$

$p=9(\frac{81}{p})$

$p^2=9(81)$

$p=27$

put p=27 in (1) we get

$\mplies\:q=\frac{324}{27}$

$\mplies\:q=12$

$\therefore$

A alone can finish a work in 18+27 = 45 days

B alone can finish a work in 18+12 = 30 days