Question

Ranjana wants to distribute 540 oranges among some students. If 30 students were more, each would get 3 oranges less. Find the number of students.

Manisha wants to distribute 540 bananas among some students. If 30 students were more, each would get 3 bananas less. Find the number of students.

Answer 1

Let the total number of students be x.

Total oranges = 540

Orange each student gets will be `540/x`.

If 30 more students are there so, the total number of students will be x + 30.

The number of oranges per person will be `540/(x + 30)`.

If 30 students were more each would get 3 oranges less = `540/x - 3`

`540/(x + 30) = 540/x - 3`

⇒ `3 = 540(1/x - 1/(x + 30))`

⇒ `1 = 540/3 ((x + 30 - x)/(x(x + 30)))`

⇒ `1 = 180 ((30)/(x^2 + 30x))`

⇒ x² + 30x = 5400

⇒ x² + 30x − 5400 = 0

⇒ x² + 90x − 60x − 5400 = 0

⇒ x(x + 90) − 60(x + 90) = 0

⇒ (x + 90)(x − 60) = 0

⇒ x + 90 = 0 or x – 60 = 0

⇒ x = – 90 or x = 60

But number of students cannot be negative so, the number of students is 60.

Answer 2

Let the number of students be x.

Then each will get `540/x` bananas.

30 students were more.

∴ the number of students is (x + 30).

∴ each will get `540/(x + 30)` bananas.

From the given condition,

`540/x - 540/(x + 30) = 3`

∴ `540 (1/x - 1/(x + 30)) = 3`

∴ `180[(x + 30 - x)/(x(x + 30))] = 1`    ...(Dividing both the sides by 3)

∴ 180 × 30 = x(x + 30)

∴ x² + 30x = 5400

∴ x² + 30x − 5400 = 0

∴ x² + 90x − 60x − 5400 = 0        ...[−5400 = 90 × (−60)]

∴ x(x + 90) − 60(x + 90) = 0

∴ (x + 90)(x − 60) = 0

∴ x + 90 = 0 or x − 60 = 0

∴ x = −90 or x = 60

But the number of students cannot be negative

∴ x = −90 is unacceptable.

∴ x = 60

∴ The number of students is 60.