Given: 75 boys finish a work in 24 days while 2 men do in a day same work as 3 boys do in a day

i.e., 75B do the work 24D……….. (i)

And 2M = 3B………… (ii)

Thus, 1B = 2/3M

75B = (2/3 × 75) M

∴ 75B = 50M…… (iii)

∴ 50M will do the work in 24 days.

Now according to formulae, $(\frac{{{{\rm{M}}_1} \times {{\rm{D}}_1} \times {{\rm{H}}_1}}}{{{{\rm{W}}_1}}} = \;\frac{{{{\rm{M}}_2} \times {{\rm{D}}_2} \times {{\rm{H}}_2}}}{{{{\rm{W}}_2}}})$

Where, M = No. of men,

D = no. of days

H = no. of hours

W = amount of work

Now, let the no. of men required to complete twice the work be x,

Then, $(\frac{{50{\rm{\;}} \times {\rm{\;}}24}}{{\rm{w}}} = \;\frac{{x\; \times 15}}{{3{\rm{w}}}})$

∴ x = 240