An NGO named AKASH distributed some books among the children of an orp

1.	An NGO named AKASH distributed some books among the children of an orphanage. If the total number of children are increased by 5, then each children will get 2 book less. If total number of children are decreased by 10, then each children will get 10 books more. Find the total number of books distributed in the orphanage.1. 2002. 1503. 2504. 100
Answer» Correct Answer - Option 1 : 200 Given: If the total number of children are increased by 5, then each children will get 2 book less. If total number of children are decreased by 10, then each children will get 10 books more. Calculation: Let the total number of children be x and each children get books be y Total books = x × y According to question If children = x + 5, and books per child = y – 2 Then (x + 5) × (y – 2) = x × y ⇒ x × y – 2x + 5y – 10 = x × y ⇒ 2x – 5y = -10 ---- (1) If children = x – 10, and books per child = y + 10 Then (x – 10) × (y + 10) = x × y ⇒ x × y + 10x – 10y – 100 = x × y ⇒ 10x – 10y = 100 ⇒ x – y = 10 ---- (2) Subtracting eq. (1) from 5 × eq. (2) ⇒ 5 × (x – y) – (2x – 5y) = 5 × 10 – (-10) ⇒ 5x – 5y – 2x + 5y = 50 + 10 ⇒ 3x = 60 ⇒ x = 20 Put the value of x in eq. (2) ⇒ 20 – y = 10 ⇒ y = 10 Total book = x × y ⇒ 20 × 10 ⇒ 200 ∴ The total number of books distributed in the orphanage is 200.

An NGO named AKASH distributed some books among the children of an orphanage. If the total number of children are increased by 5, then each children will get 2 book less. If total number of children are decreased by 10, then each children will get 10 books more. Find the total number of books distributed in the orphanage.1. 2002. 1503. 2504. 100

Answer» Correct Answer - Option 1 : 200

Given:

If the total number of children are increased by 5, then each children will get 2 book less.

If total number of children are decreased by 10, then each children will get 10 books more.

Calculation:

Let the total number of children be x and each children get books be y

Total books = x × y

According to question

If children = x + 5, and books per child = y – 2

Then (x + 5) × (y – 2) = x × y

⇒ x × y – 2x + 5y – 10 = x × y

⇒ 2x – 5y = -10 ---- (1)

If children = x – 10, and books per child = y + 10

Then (x – 10) × (y + 10) = x × y

⇒ x × y + 10x – 10y – 100 = x × y

⇒ 10x – 10y = 100

⇒ x – y = 10 ---- (2)

Subtracting eq. (1) from 5 × eq. (2)

⇒ 5 × (x – y) – (2x – 5y) = 5 × 10 – (-10)

⇒ 5x – 5y – 2x + 5y = 50 + 10

⇒ 3x = 60

⇒ x = 20

Put the value of x in eq. (2)

⇒ 20 – y = 10

⇒ y = 10

Total book = x × y

⇒ 20 × 10

⇒ 200

∴ The total number of books distributed in the orphanage is 200.