JAMIA 2026 — Reasoning PYQ

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Question

JAMIA 2026 — Reasoning PYQ

JAMIA | Reasoning | 2026

X, Y, and Z together can complete a work in 6 days. X alone takes 12 days and Y alone takes 18 days to complete the same work. In how many days will X and Z together complete this work?

Choose the correct answer:

Explanation

Method 1: The LCM (Total Work) Method

1. Find the Total Work:

Let the total work be the Least Common Multiple (LCM) of the given number of days (6, 12, and 18).

$Total Work = LCM (6, 12, 18) = 36 units$

2. Calculate individual efficiencies (work done per day):

Efficiency of $(X + Y + Z) = \frac{36}{6} = 6 units/day$
Efficiency of $X = \frac{36}{12} = 3 units/day$
Efficiency of $Y = \frac{36}{18} = 2 units/day$

3. Find the efficiency of Z:

$Efficiency of Z = Efficiency of (X + Y + Z) - (Efficiency of X + Efficiency of Y)$

$Efficiency of Z = 6 - (3 + 2) = 6 - 5 = 1 unit/day$

4. Find the combined efficiency of X and Z:

$Efficiency of (X + Z) = Efficiency of X + Efficiency of Z$

$Efficiency of (X + Z) = 3 + 1 = 4 units/day$

5. Calculate the time taken by X and Z together:

$Days taken by (X + Z) = \frac{Total Work}{Efficiency of ( X + Z )}$

$Days taken by (X + Z) = \frac{36}{4} = 9 days$

Correct Answer

The correct option is (d) 9.