Two workers A and B can complete a work in 35 days and 45 days, respectively. Initially, both A and B started working together. However, A left after some days and B alone completed the remaining work in 29 days. Find the number of days that A and B worked together.

Correct option is B

Given:
Two workers A and B can complete a work in 35 days and 45 days
B alone completed the remaining work in 29 days
Formula Used:
Work = Time × Efficiency
Solution:
Let total work = LCM of 35 and 45 = 315 unit
Efficiency of A  = $$\frac{315}{35} = 9 \text{ units/day} \\$$​​

Efficiency of B  = $$\frac{315}{45} = 7 \text{ units/day}$$​​
Let the number of days for which A and B worked together be x.
Efficency when A and B work together = 9 + 7 = 16
Then, x × 16 + 29 × 7 = 315
=> 16x = 315 - 203 = 112
Or, x = $$\frac {112}{16}$$= 7 days.
∴ A and B worked together for 7 days. 
Alternate Solution:

Let total work = LCM of 35 and 45 = 315 unit
Efficiency of A  = $$\frac{315}{35} = 9 \text{ units/day} \\$$​​

Efficiency of B  = $$\frac{315}{45} = 7 \text{ units/day}$$ 
Work done by B in 29 days = 29 × 7 = 203 unit
Remaining Work = 315-203 = 112 unit 
This work has to be done by A and B together in = $$\frac {112}{16}$$​= 7 days.

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