Question

28 workers can build a piece of machinery in 50 days. How many workers in 35 days
A 49
B. 35
C 045
d 40​

Answer 1

Given :

• 28 workers can build a piece of machinery in 50 days

Aim :

• To find the number of workers required to build a piece of machinery in 35 days.

Solution :

• According to the question, 28 workers can build a piece of machinery in 50 days. We have to find how many workers can finish the same in 35 days. Here, the values are in inverse proportion.

Inverse proportion :

The proportion in which, when one value increases ↑, the other decreases ↓ is said to be Inverse proportion.

• With the number is days decreasing, the number of men required to complete the work increases.

In inverse proportion,

$\longrightarrow \sf x_{1} \times y_{1} = y_2 \times x_{2}$

$\longrightarrow \sf \dfrac{x_{1} \times y_{1}}{x_{2}} = y_{2}$

$\longrightarrow \sf \dfrac{y_{2} \times x_{2}}{x_{1}} = y_{1}$

The same applies for the values for x¹ and x² respectively.

$\sf x \: \: \: \: \: \: \: y \\ 28 \: \: \: \: \: 50 \\ x_2 \: \: \: \: \: \: \: 35$

Here, let us take the number of workers as x and the number of days as y.

In order to find the value of x, we have to equate the product of 28 × x and 50 × 35

$\implies \sf 35 \times x_{2} = 50 \times 28$

$\implies \sf 35x_{2} = 1400$

Transposing 35 to the RHS (Right hand side of the equation,)

$\implies \sf x_{2} = \dfrac{1400}{35}$

Reducing to the lowest terms,

$\implies \sf x_{2} = 40$

Therefore, option (d) 40 workers is correct ✓

More info :

Direct proportion :

The proportion in which, both the values decrease ↓ or increase ↑ according.

In direct proportion,

$\longrightarrow \sf x_{1} \times y_{2} = x_{2} \times y_{1}$

Answer 2

ANSWER

40 WORKERS

Step-by-step explanation:

BY UNITARY MEATHOD

NOTE: THE VALUE WHICH YOU HAVE TO FIND ALWAYS KEEP IT IN THE RIGHT SIDE

LIKE HERE WE HAVE TO FIND THE NUMBER OF WORKERS SO I HAD PUT THAT VALUE RIGHT SIDE

SOLUTION

50 days to complete a work is taken by =28 workers

1 day to complete a work is taken by =28 ×50 =1400 workers ( here we multiply because here you can see that work is completed so fast only in one day which means there are more workers)

35 days is taken by =

$\frac{1400}{35} = 40$

40 workers

(And here we divide because as the time increase workers decrease)

by proportion method

let the no. of workers to complete a work in 35 days=x

IT IS IN INVERSE PROPORTION AS THE DAYS DECREASE THE NO. OF WORKERS WILL INCREASE

so ATQ

35:28::50:x

product of means=product of extremes

so 35x=50×28

x=

$\frac{50 \times 28}{35} = 40$

40 workers