A

([latex]\frac {1}{5} + \frac {1}{4}[/latex]) = [latex]\frac {20}{9} + \frac {90}{100} = 2[/latex]

C

Efficiency (A : B) = 5 : 4
Number of days(A : B) = 4x : 5x = 4x : 25
∴ Number of days required by A to finish the work alone = 4x
= 4 x 5 = 20.
A and B work together for last 5 days = 5 x 9 = 45 %
Efficiency of A = 5% and B’s efficiency = 4 %
∴ No. of days taken by A to complete 55% work = [latex]\frac {55}{5}[/latex] = 11 days

B

[latex]\frac {3}{4}[/latex] × (x-2)x = (x+7)(x-10)
x – 6x – 280 = 0
x = 20; x = -14
(x-2)x = 18 × 20 = 360
360 = 30 × y
y = 12 days

B

[latex]\frac {1}{8} + \frac {1}{12} \frac {1}{C} + \frac {1}{4}[/latex] we get C = 24 days
Now efficiency of A, B and C are in the ratio of [latex]\frac {1}{8} : \frac {1}{12} : \frac {1}{24}[/latex]
3 : 2 : 1 so share of C is [latex]\frac {1}{6} \times 1200 = 200 [/latex]

B

Q is 25 percent more efficient so he will complete the work in 16 days
[latex]\frac {1}{20} + \frac {1}{16} \times t = \frac {1}{2}[/latex]
[latex]\frac {4 + 5}{80} \times t = \frac {1}{2}[/latex]
[latex] t = \frac {1}{2} \times \frac {80}{9} = \frac {40}{9}[/latex]