Problem 9 - Set 1 - Try Out - General Reasoning - SNBT

Number 9

Approaching the holidays, Father plans to paint the house. If Father paints alone, he needs $20$ hours. If he works together with Uncle Udin, they only need $4$ hours. If the first $8$ hours are done by Father alone and then the rest is done by Uncle Udin alone, the total time required for Uncle Udin to complete the work is...

1 hour

1 hour 30 minutes

2 hours

2 hours 30 minutes

3 hours

Explanation

We can solve this problem using the concept of work rate. Let the total job of painting the house be $1$ unit of work.

Determining Uncle Udin's Work Rate

It is known that Father alone takes $20$ hours, so Father's work rate ( $V_F$ ) is:

V_F = \frac{1}{20} \text{ job/hour}

It is known that working together takes $4$ hours. If $V_U$ is Uncle Udin's work rate, then:

\begin{aligned} V_{total} &= V_F + V_U \\ \frac{1}{4} &= \frac{1}{20} + V_U \\ V_U &= \frac{1}{4} - \frac{1}{20} \\ V_U &= \frac{5}{20} - \frac{1}{20} \\ V_U &= \frac{4}{20} = \frac{1}{5} \text{ job/hour} \end{aligned}

So, Uncle Udin can complete the job alone in $5$ hours.

Calculating Remaining Work

Father works alone for the first $8$ hours. The portion of work completed by Father is:

\text{Father's Work} = 8 \times \frac{1}{20} = \frac{8}{20} = \frac{2}{5} \text{ part}

The remaining work to be done by Uncle Udin is:

\text{Remaining} = 1 - \frac{2}{5} = \frac{3}{5} \text{ part}

Calculating Uncle Udin's Time

The time required for Uncle Udin to complete the remaining work is:

\text{Time} = \frac{\text{Remaining Work}}{\text{Udin's Rate}} = \frac{\frac{3}{5}}{\frac{1}{5}} = 3 \text{ hours}

Thus, Uncle Udin needs 3 hours to complete the remaining work.

Command Palette

Number 9

Explanation

Determining Uncle Udin's Work Rate

Calculating Remaining Work

Calculating Uncle Udin's Time