AFCAT I 22 Jan 2025 Shift 1 Paper

Work done by Ajay and Vijay per day together = Ajay's rate + Vijay's rate
Work done by Vijay alone in 27 days = Vijay's daily rate ×27 days
Use the concept of work done to set up an equation and solve for the number of days Ajay worked before leaving.
Work rate of Ajay:
⇒ Ajay's rate =1∕25 (work/day)
Work rate of Vijay:
⇒ Vijay's rate =1∕40 (work/day)
Work rate of Ajay and Vijay together:
⇒ Combined rate =(1∕25)+(1∕40)
Find a common denominator and add:
⇒ Combined rate =(8+5)∕200
⇒ Combined rate = 13∕200 (work/day)
Work done by Vijay alone in 27 days:
⇒ Work done by Vijay =27×(1∕40)
⇒ Work done by Vijay = 27/40
Let's say Ajay worked for x days. During these x days, both Ajay and Vijay were working.
Work done by Ajay and Vijay together in x days:
⇒ Work done together =x×(13∕200)
The total work = Work done by Ajay and Vijay together + Work done by Vijay alone:
⇒1=(x×13∕200)+27∕40
Convert 27/40 to a fraction with a denominator of 200 :
⇒27∕40=(27×5)∕(40×5)=135∕200
Substitute and solve for x :
⇒1=(13x∕200)+135∕200
Multiply both sides by 200 to clear the fractions:
⇒200=13x+135
Subtract 135 from both sides:
⇒65=13x
Divide both sides by 13 :
⇒x=65∕13
⇒x=5