A sum of Rs 27000 was divided equally among a certain number of persons. Had there been 20 more persons, each would have got Rs 480 less. The number of persons, initially, wasa)24b)25c)45d)48Correct answer is option 'B'. Can you explain this answer?

Question

Answer

let number of persons = n
Indivisual share = 27000/n

⇒ n² + 20n – 1125 = 0
⇒ (n + 45)(n – 25) = 0
⇒ n = 25

Answer

To solve this problem, let's break it down into steps:

Step 1: Let's assume the initial number of persons is 'x'.

Step 2: Since the total sum of money is divided equally among 'x' persons, each person initially receives Rs 27000/x.

Step 3: According to the problem, if there were 20 more persons, each person would receive Rs 480 less. This means that if the number of persons was 'x + 20', each person would receive Rs (27000/x) - 480.

Step 4: Now, we can form an equation based on the given information. The equation is:

(27000/x) - 480 = (27000/(x + 20))

Step 5: To solve this equation, let's simplify it by multiplying both sides by x(x + 20) to eliminate the denominators:

27000(x + 20) - 480x(x + 20) = 27000x

Step 6: Expanding and simplifying the equation further:

27000x + 540000 - 480x^2 - 9600x = 27000x

Step 7: Rearranging the equation and simplifying:

480x^2 + 9600x - 540000 = 0

Step 8: Factoring the quadratic equation:

480(x^2 + 20x - 1125) = 0

Step 9: Now, let's solve the quadratic equation:

x^2 + 20x - 1125 = 0

Step 10: Factoring the quadratic equation:

(x + 45)(x - 25) = 0

Step 11: Solving for 'x', we get:

x + 45 = 0 or x - 25 = 0

x = -45 or x = 25

Step 12: Since the number of persons cannot be negative, we discard the solution x = -45.

Step 13: Therefore, the initial number of persons is x = 25.

Hence, the correct answer is option 'B' (25).

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