What you have written down is correct, but I feel like you do not fully understand how you are manipulating the expressions to get the answer. Here's my answer building on what you have done with explanations. It would make more sense to say that in $\text{LCM}(x+6, x+15, 2x) = (x+6)(x+15)(2x)$ hours:
so when $A,B,C$ work together, they can do: $$(x+15)(2x) + (x+6)(2x) + (x+6)(x+15)$$ $$= 5x^2 + 63x + 90$$ jobs in the given time, as you have said. Since it is assumed that each person works at a constant rate, then the $\text{(number of jobs)}/\text{(time)}$ is always constant. But $A,B,C$ together must do $1$ job in $x$ hours according to your first assumption, so this means that: $$\frac{5x^2+63x+90 \text{ jobs}}{(x+6)(x+15)(2x) \text{ hours}} = \frac{1\text{ jobs}}{x \text{ hours}}$$ and now your job is to find $x$. No worries! We‘ve got your back. Try BYJU‘S free classes today! No worries! We‘ve got your back. Try BYJU‘S free classes today! Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses No worries! We‘ve got your back. Try BYJU‘S free classes today! No worries! We‘ve got your back. Try BYJU‘S free classes today!
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Given: A can do a piece of work in 4 hours. B and C together can do it in 3 hours. A and C together can do it in 2 hours. Concept Used: Work done = 1/Time Or Work done = Efficiency × Time Calculation: A can do a piece of work in 4 hours. A's 1 day work = 1/4 A and C together can do it in 2 hours. (A + C)'s 1 day work = 1/2 C's 1 day work = 1/2 - 1/4 = 1/4 B and C together can do it in 3 hours. (B + C)'s 1 day work = 1/3 B's 1 day work = 1/3 - 1/4 = 1/12 Time taken by B to complete the work = 12 days ∴ Time taken by B to complete the work is 12 days.
A can do a piece of work in 4 hours. B and C together can do it in 3 hours. A and C together can do it in 2 hours. Total work done = LCM of days = 12 units Efficiency of A = 3 units Efficiency of A + C = 6 units Efficiency of C = 6 - 3 = 3 units Efficiency of B + C = 4 units Efficiency of B = 4 - 3 = 1 units Time taken by B to complete the work = 12/ 1 = 12 days ∴ Time taken by B to complete the work is 12 days. India’s #1 Learning Platform Start Complete Exam Preparation
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A can do a piece of work in 4 hours, B and C can do it in 3 hours. A and C can do it in 2 hours. How long will B alone take to do it? [A]8 hours [B]24 hours [C]10 hours [D]12 hours
12 hours A’s one hour’s work $latex = \frac{1}{4}&s=1$ (B + C)’s one hour’s work $latex = \frac{1}{3}&s=1$ (A + C)’s one hour’s work $latex = \frac{1}{2}&s=1$ ∴ C’s one hour’s work $latex = \frac{1}{2}-\frac{1}{4} = \frac{2-1}{4} = \frac{1}{4}&s=1$ B’s one hour’s work $latex = \frac{1}{3}-\frac{1}{4} = \frac{4-3}{12} = \frac{1}{12}&s=1$ Hence B alone can do the work in 12 hours, so option [D] is correct answer. |
Can do a piece of work in 4 hours B and C together in 3 hours and A and C together in 2 hours how long will b alone take to do it?
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