Question

P can do 2/5 part of some work in 10 days . If P and Q can do 1/3 part of the some work in 5 day . What is the ratio of their efficiencies​

Answer 1

Answer:

Ratio of efficiences of P and Q is  3 :  2

Step-by-step explanation:

P can do $\frac{2}{5}$ of work in 10 days

P can do complete work in $10 \times \frac{5}{2} = 25\hspace{0.1cm}days$

Thus, P's 1 day work $= \frac{1}{25}$

Now, (P + Q) can do $\frac{1}{3}$ of work in5 days

(P + Q) can do complete work in $5 \times \frac{3}{1} = 15\hspace{0.1cm}days$

Thus, (P + Q)'s 1 day work $= \frac{1}{15}$

Total work is LCM of 25 and 15 $=75\hspace{0.1cm}parts$

P's 1 day work $=\frac{75}{25} = 3\hspace{0.1cm}parts$

(P + Q)'s 1 day work $=\frac{75}{15} = 5\hspace{0.1cm}parts$

Thus, Q's 1 day work $= 5 - 3 = 2\hspace{0.1cm}parts$

We have,

$2p = 75\\\ p = \frac{75}{2}\\\\ p = 37.5 days$

Thus, B can do complete work in 37.5 days

Now, ratio of efficiency of P and Q

$Efficiency\hspace{0.1cm}Ratio = \frac{Efficiency \hspace{0.1cm}of\hspace{0.1cm} P}{Efficiency \hspace{0.1cm}of\hspace{0.1cm} Q}\\\\Efficiency\hspace{0.1cm}Ratio = \frac{\frac{1}{25}}{\frac{1}{37.5}}\\\\ Efficiency\hspace{0.1cm}Ratio =\frac{37.5}{25} \\\\ Efficiency\hspace{0.1cm}Ratio =\frac{75}{25 \times 2}\\\\ Efficiency\hspace{0.1cm}Ratio =\frac{3}{2} \\\\ Efficiency\hspace{0.1cm}Ratio =3 : 2$