Question

A person divides some money among some students equally. If there were 5 more students, each student will get ₹ 4 less. If there were 5 students less, each student will get ₹ 6 more. Find the total money.

Answer 1

Given:

• A person divides a certain total amount of money equally among some students.
• If 5 more students are there, each student gets ₹ 4 less.
• If 5 fewer students are there, each student gets ₹ 6 more.

Step-wise calculation:

1. Let the number of students be (x).

2. Let the amount each student gets be ₹ (y).

3. Therefore, total money = x × y.

4. If there were 5 more students, total students = x + 5 and each one gets ₹ (y – 4).

(x + 5)(y – 4) = x × y

⇒ xy – 4x + 5y – 20 = xy

Simplifying,

–4x + 5y = 20

⇒ 5y = 4x + 20

⇒ `y = (4x + 20)/5`

5. If there were 5 fewer students, total students (x – 5) and each one gets ₹ (y + 6).

(x – 5)(y + 6) = x × y

⇒ xy + 6x – 5y – 30 = xy

Simplifying,

6x – 5y = 30

6. Substitute (y) from step 4 into the equation from step 5:

`6x - 5((4x + 20)/5) = 30`

6x – (4x + 20) = 30 

6x – 4x – 20 = 30 

2x = 50

⇒ x = 25

7. Find (y) by substituting (x = 25) into `( y = (4x + 20)/5)`: 

`y = (4(25) + 20)/5`

`y = (100 + 20)/5`

`y = 120/5`

y = 24

8. Total money is x × y = 25 × 24 = ₹ 600.

The total money divided among the students is ₹ 600.