Question

To deliver an order on time, a company has to make 25 parts a day. After making 25 parts per day for 3 days, the company started to produce 5 more parts per day, and by the last day of work 100 more parts than planned were produced. Find how many parts the company made and how many days this took.

Answer 1

For 3 days the parts made were = 25×3 

⇒ 75 parts were made in 3 days 

Now after producing the 75 parts in 3 days the company started producing 5 more parts a day 

⇒ 25+5 = 30 parts (30 parts each day after the producing 75 parts)

Let us assume that the days worked in the company = z

From the given observation of the parts made :

⇒ 3×25+(x−3)×30=75+30(x−3) 

(here in the above equation 3 and -3 will get cancelled)

⇒ 25x=75+30(x-3)-100 

(here in the above step we will multiply 30 with x and even -3)

⇒ 25x=75+30x-90 -100 

(now bring both -90 and -100 and even 75 towards left hand side) and ( 25x towards right hand side)

⇒ 90+100 -75 = 25x-30x

⇒ 190-75 = 5x 

⇒ 115 = 5x 

⇒ x = $\frac{115}{5}$

⇒ x = 23 

∴ the number of days worked will be 23 days by the company 

⇒ the parts produced will be 23×25+100

∴ the parts produced by the company = 675 

Answer 2

First, it was producing 25 parts a day.

Parts produced in first 3 days = 25 × 3 = 75

So, it produced 75 parts in first 3 days.

Now, let the number of days more it kept producing be 'x'

So, parts produced during the rest days = (25 + 5)x = 30x


Since it started producing 5 more parts per day later.

Given that the total number of extra parts produced were 100.

So, the sum of the total extra parts produced should add up to 100. That would be

(30x + 75) - 100 = 25(x +3)
30x - 25 = 25x + 75
5x = 100
x = 20

Total number of days it worked = 20 + 3 = 23

So, it made 30x + 75 parts
i.e. (30 × 20) + 75 = 600 + 75 = 675 parts