Suresh can do a work in 10 days working 1 hour a day. Shalu can do the same work in 2 days working 5 hours a day. How many hours do they need to work together in a day to complete the same work in 10 days?

0.5 hours 

The formula for work for different men is  ⇒ \(\frac{M_1\;×\;D_1\;×\;H_1\;×\;E_1}{M_2\;×\;D_2\;×\;H_2\;×\;E_2}\) = \(\frac{W_1}{W_2}\)

Since work is same, $W_1 = W_2$

The equation becomes,

 \(\frac{1\;×\;10\;×\;1\;×\;E_1}{1\;×\;2\;×\;5\;×\;E_2}\) = 1

⇒ $\frac{E_1}{E_2}$ = 1

⇒ $E_1 = E_2$

Together, their efficiency becomes 2

To complete the same work in 10 days with efficiency 2, they need

⇒  \(\frac{10\;×\;1\;×\;1}{10\;×\;H_2\;×\;2}\) = 1

                     (Using the formula for first when Suresh works alone and when they work together)

⇒  $H_2$ = 0.5 hours