Time and Work Quiz Set 010

Use the shortcut formula. If A, B, C can independently complete the job in x, y and z days, and A joins after n days, the work is completed in ${xyz}/{xy + yz + zx}$ × $(1 + n/x)$ days. Putting the various values x = 5, y = 15, z = 13, n = 2, and simplifying, we get ${273/67}$, which is same as: $4{5/67}$.

If B takes x days. The total job is A's work in 4 days + B's work in x days = $6/16$ + $x/64$ = 1. Solving, we get x = 40 days.

Since the work force is being doubled proportionately, the time is halved = 8 days.

Let us first calculate the one day work of B. One day work of A is given as $1/18$. If B is 20% efficient, then one day work of B is $1/18$ × $120/100$ = $1/15$. Putting x = 18 and y = 15 in the shortcut method, we get ${xy}/{x + y}$ = ${90/11}$, which is same as: $8{2/11}$.

If m₁ men can do a task in d₁ days, and m₂ in d₂, then we must have m₁ × d₁ = m₂ × d₂. Putting m₁ = 80, d₁ = 16 and d₂ = 10, we get m₂ = 128.