CUET UG 2025 — General Test Arithmetic

A can complete the work in 16 days, working 6 hours a day.

Total hours A needs to complete the work:

$$16 \times 6$$16×6

$= 96$=96 hours

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B can complete the work in 12 days, working 9 hours a day.

Total hours B needs to complete the work:

$$12 \times 9$$12×9

$= 108$=108 hours

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A completes $\dfrac{1}{96}$961​ of the work in 1 hour.

B completes $\dfrac{1}{108}$1081​ of the work in 1 hour.

Together in 1 hour:

$$\dfrac{1}{96} + \dfrac{1}{108}$$961​+1081​

Finding LCM of 96 and 108:

LCM $= 864$=864

$$\dfrac{1}{96} = \dfrac{9}{864}$$961​=8649​

$$\dfrac{1}{108} = \dfrac{8}{864}$$1081​=8648​

$$\dfrac{9}{864} + \dfrac{8}{864}$$8649​+8648​

$= \dfrac{17}{864}$=86417​ of the work per hour

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Working 8 hours a day together, work completed in 1 day:

$$8 \times \dfrac{17}{864}$$8×86417​

$$= \dfrac{136}{864}$$=864136​

$= \dfrac{17}{108}$=10817​ of the work

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Total days needed to complete the work:

$$1 \div \dfrac{17}{108}$$1÷10817​

$$= 1 \times \dfrac{108}{17}$$=1×17108​

$= \dfrac{108}{17}$=17108​ days

Therefore, they can complete the work in $\dfrac{108}{17}$17108​ days.