Question

Humans and robots can both perform a job but at different efficiencies. Fifteen humans and five robots working together take thirty days to finish the job, whereas five humans and fifteen robots working together take sixty days to finish it. How many days will fifteen humans working together (without any robot) take to finish it?

36
32
45
40

Answer 1

Answer:

♠  The correct option is B.

Step-by-step explanation:

Let the rates of work of each human and each robot be H and R respectively.

15H + 5R = 1/30

5H + 15R = 1/60

Multiplying first equation by 3,

45H + 15R = 1/10

Subtracting the second equation,

40H = 1/10 - 1/60

40H = 1/12

H = 1/480

In a day, 15 humans can complete 15H i.e. 1/32th of the job.

15 humans can complete the job in 32 days.

Answer 2

Question :--- in how many days 15 Humans can complete whole work ....

$\bold{Given}\begin{cases}\sf{</strong><strong> </strong><strong>15</strong><strong>\</strong><strong>:</strong><strong>Humans</strong><strong> + 5</strong><strong>\</strong><strong>:</strong><strong> </strong><strong>robots\</strong><strong>:</strong><strong>can\</strong><strong>:</strong><strong> </strong><strong>do\</strong><strong>:</strong><strong> </strong><strong>the\</strong><strong>:</strong><strong> </strong><strong>job\</strong><strong>:</strong><strong> </strong><strong>in\</strong><strong>:</strong><strong> 30 days</strong><strong>}\\\sf{</strong><strong>5</strong><strong>\</strong><strong>:</strong><strong> humans + </strong><strong>\</strong><strong>:</strong><strong>15</strong><strong>\</strong><strong>:</strong><strong> robots </strong><strong>\</strong><strong>:</strong><strong>can\</strong><strong>:</strong><strong> do</strong><strong>\</strong><strong>:</strong><strong>it</strong><strong> </strong><strong>\</strong><strong>:</strong><strong>in\</strong><strong>:</strong><strong> 60</strong><strong>\</strong><strong>:</strong><strong>days</strong><strong>}</strong><strong>\end{cases}$

$\huge\boxed{\fcolorbox{cyan}{grey}{</strong><strong>Solution</strong><strong>:</strong><strong>--</strong><strong>}}$

Let humans denoted by = H

robots denoted by = R .

A/q,

30(15H + 5R) = 60(5H + 15R)

15H + 5R = 10H + 30R

5H = 25R

$\frac{h}{r} = \frac{25}{5} = \frac{5}{1}$

so, efficiency of 1 human = 5

efficiency of 1 robot = 1

so,

Total work = 30(15H+5R) = 30(15*5+5*1) = 30(75+5) = 30*80 = $\large\red{\boxed{\sf </strong><strong>2</strong><strong>4</strong><strong>0</strong><strong>0</strong><strong>units</strong><strong>}}$

Now this work is done by 15 humans only ...

Their one day work = 15*5 = 75 units .

so,

Time they will take to complete whole work = $\huge{\frac{</strong><strong>2</strong><strong>4</strong><strong>0</strong><strong>0</strong><strong>}{</strong><strong>7</strong><strong>5</strong><strong>}}$ = $\huge\underline\purple{\mathcal </strong><strong>3</strong><strong>2</strong><strong>\</strong><strong>:</strong><strong>days</strong><strong>}</strong><strong>$

$\huge\underline\mathfrak\green{Hope\:it\:Helps\:You}$