CAT Quantitative Aptitude Questions | CAT Time and Work questions

The question is from Time and Work. Here, work is getting interrupted by continuous kidnapping, Still, the work gets done :).

Question 24: Amar, Akbar and Anthony set out to complete a work. Anthony being the eldest would take 1 day less than Amar if he were to complete the work alone. All three together could complete the work in a day. However, Anthony was kidnapped by Shakal. Amar and Akbar began the work in his absence. After a day, Amar was also kidnapped. Akbar took 3 more days to finish the work. How much portion of the work Anthony could do in a day?

1. \\frac{2}{3}\\)
2. \\frac{1}{6}\\)
3. \\frac{1}{2}\\)
4. \\frac{1}{3}\\)

Explanatory Answer

Method of solving this CAT Question from Pipes Cisterns and Work Time: We can do trial and error to arrive at the answer!

Let Amar take x days and Akbar take y days to finish the work. So, Anthony would take x-1 days to complete the work alone.
Therefore, as per question,
\\frac{1}{x}\\) + \\frac{1}{(x-1)}\\) + \\frac{1}{y}\\) = 1 …………………(1)
Also given, (\\frac{1}{x}\\) + \\frac{1}{y}\\) + \\frac{3}{y}\\)) = 1
=> \\frac{1}{x}\\) + \\frac{4}{y}\\) = 1
=> \\frac{1}{y}\\) = \\frac{1}{4}\\) - \\frac{1}{4x}\\) ………………………(2)
Putting in equation (1),
=> \\frac{1}{x}\\) + \\frac{1}{(x-1)}\\) + \\frac{1}{4}\\) - \\frac{1}{4x}\\) = 1
=> \\frac{1}{x}\\) + \\frac{1}{(x-1)}\\) - \\frac{1}{4x}\\) = \\frac{3}{4}\\)
Now using option analysis,
a) Work done by Anthony in 1 day = \\frac{1}{(x-1)}\\) = \\frac{2}{3}\\) =) 3 = 2x - 2 =) x = \\frac{5}{2}\\) = 2.5
L.H.S of (3) => \\frac{1}{2.5}\\) + \\frac{1}{1.5}\\) - \\frac{1}{10}\\) = 0.4 + 0.66 – 0.1 ≠ 0.75
b) \\frac{1}{(x-1)}\\) = \\frac{1}{6}\\) =) x = 7 L.H.S of (3) = \\frac{1}{7}\\) + \\frac{1}{6}\\) - \\frac{1}{28}\\) ≠ \\frac{3}{4}\\)
c) \\frac{1}{(x-1)}\\) = \\frac{1}{2}\\) =) x = 3 L.H.S of (3) = \\frac{1}{3}\\) + \\frac{1}{2}\\) - \\frac{1}{12}\\) = \\frac{(4 + 6 – 1)}{12}\\) = \\frac{9}{12}\\) = \\frac{3}{4}\\)

The question is "How much portion of the work Anthony could do in a day?"

Hence, the answer is "\\frac{1}{2}\\)".

Choice C is the correct answer.