JAMIA 2026 — Reasoning PYQ

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Question

JAMIA 2026 — Reasoning PYQ

JAMIA | Reasoning | 2026

If X completes half of a work in 9 days, and Y completes one-third of the same work in 12 days. In how many days will X and Y together complete this work?

Choose the correct answer:

Explanation

1. Find the total time taken by X and Y individually to complete the entire work:

For X: X completes $\frac{1}{2}$ of the work in $9 days$ .
$Total time taken by X (T_{X}) = 9 \times 2 = 18 days$
For Y: Y completes $\frac{1}{3}$ of the work in $12 days$ .
$Total time taken by Y (T_{Y}) = 12 \times 3 = 36 days$

2. Calculate Total Work using the LCM Method:

Let the total units of work be the Least Common Multiple (LCM) of the days taken by X and Y.

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

3. Determine Individual Efficiencies (Work done per day):

$Efficiency of X = \frac{36}{18} = 2 units/day$
$Efficiency of Y = \frac{36}{36} = 1 unit/day$

4. Calculate Time Taken Together:

$Combined Efficiency of (X + Y) = 2 + 1 = 3 units/day$

$Days taken by both to finish the work = \frac{Total Work}{Combined Efficiency}$

$Days taken = \frac{36}{3} = 12 days$

Correct Answer

The correct option is (c) 12.