Question

Ramu and Sita together can complete a project in 6 days. If Ramu alone can complete the same project in 15 days, inhow many days can Sita alone complete the project? (in hours)​

Answer 1

Answer:

10 days

Step-by-step explanation:

Given :

1) No. of days it takes Ramu and Sita to complete the work = 6 days

2) No. of days it takes Ramu alone to complete the work = 15 days

To Find:

No. of days Sita alone will take to complete the work(in hours)

Solution:

i) Quantity of work done by Ramu and Sita together in 1 day :

$\frac{1 \: day}{total \: number \: of \: days \: taken}$

=

$\frac{1}{6}$

ii) Quantity of work done by Ramu alone in 1 day:

$\frac{1 \: day}{total \: number \: of \: days}$

=

$\frac{1}{15}$

iii) Thus,

Quanity of work done by Sita in 1 day:

(Quantity of work done by Ramu and Sita together in 1 day) - (Quantity of work done by Ramu alone in 1 day)

=

$\frac{1}{6} - \frac{1}{15}$

=

$\frac{15 - 6}{90}$

=

$\frac{9}{90}$

=

$\frac{1}{10}$

So,

Quanity of work done by Sita in 1 day =

$\frac{1}{10}$

Thus,

It will take her 10 days to complete the project(as quanity of work done in 1 day is:

$\frac{1 \: day}{total \: number \: of \: days}$

And, we know that 1 day = 24 hours.

So, number of hours taken to complete the work by Sita alone =

$number \: of \: days \: \times \: number \: of \: hours \: in \: 1 \: day$

= 10 × 24

=

$240 \: hours$

Thus

Sita can complete the project in 10 days or 240 hours

Answer 2

Given,

Ramu and Sita together complete a project = 6 days

Ramu alone complete same project = 15 days

Solution,

One day combined work of Ramu and Sita $\[ = \frac{1}{6}\]$

One day work of Ramu $\[ = \frac{1}{{15}}\]$

One day work of Sita,

$\[\begin{array}{l} = \frac{1}{6} - \frac{1}{{15}}\\ = \frac{{15 - 6}}{{6 \times 15}}\\ = \frac{9}{{6 \times 15}}\\ = \frac{1}{{10}}\end{array}\]$

Sita alone complete work in 10 days.

Know that 1 day contain 24 hours.

$\[\begin{array}{l} = 10 \times 24\\ = 240hours\end{array}\]$

Hence Sita alone complete the project in $\[240hours\]$.