Question 717612
A can do a piece of work in 2 days as B can do in 3 days.
{{{2/A}}} = {{{3/B}}}
Cross multiply
3A = 2B
A = {{{2/3}}}B

:
 B can do as much work in 4 days as C can do in 5 days.
{{{4/B}}} = {{{5/C}}}
4C = 5B
C = {{{5/4}}}B

:
 If A, B & C finish the work together in 10 days.
Let the completed job = 1
{{{10/A}}} + {{{10/B}}} + {{{10/C}}} = 1
Replace A and C
{{{10/((2/3)B)}}} + {{{10/B}}} + {{{10/((5/4)B)}}} = 1
Multiply by {{{10/12}}}B, to clear the denominators
{{{5/4}}}(10) + {{{10/12}}}(10) + {{{2/3}}}(10) = {{{10/12}}}B
{{{50/4}}} + {{{100/12}}} + {{{20/3}}} = {{{10/12}}}B
multiply by 12
3(50) + 100 + 4(20) = 10B
150 + 100 + 80
330 = 10B
B = 330/10
B = 33 days B can finish the work alone?