A sum of money is to be distributed equally among a group of children. If there were 25 children less then each would get Tk. 1.50 more, and if there were 50 children more, each would get Tk. 1.50 less. Find the number of children and the amount of money distributed. (Algebra (Equation))

Shohan

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2025-01-04 04:42

1 Answers

Shohan

প্রশ্নে বলা হচ্ছে যে, কিছু পরিমাণ টাকা একদল বালকের মধ্যে সমানভাবে ভাগ করে দিতে হবে। ঐ দলে যদি 25 জন বালক কম থাকত, তবে প্রত্যেক 1.5 টাকা করে বেশি পেত। আবার যদি 50 জন বালক বেশি থাকত তবে প্রত্যেক 1.5 টাকা কমে কম পেত । বালকের সংখ্যা ও টাকার পরিমাণ কত?

Let, the number of children = x

and the amount of money each gets = y Tk.

∴ The total amount of money distributed = xy Tk.

So, According to question (x-25) (y +1.5) = xy . . . . . . . . . . . . . . . (i)

And (x+50) (y-1.5) = xy . . . . . . . . . . . . . . . (ii)

We get from equation (i)

$(x - 25) (y + 1.5) = x y \Rightarrow x y + 1.5 x - 25 y - 37.5 = x y \Rightarrow 1.5 x - 25 y = 37.5 \Rightarrow 3 x - 50 y = 75 . . . . . . . . . . (i i i)$

We get from equation (ii)

$(x + 50) (y - 1.5) = x y \Rightarrow x y - 1.5 x + 50 y - 75 = x y \Rightarrow - 1.5 x + 50 y = 75 . . . . . . . . . . . (i v) A d d i n g e q u a t i o n (i i i) & (i v), w e g e t \frac{3 x - 50 y = 75 - 1.5 x + 50 y = 75}{1.5 x = 150} ∴ x = \frac{150}{1.5} = 100 P u t t i n g t h e v a l u e o f x i n e q u a t i o n (i i i), w e g e t 3 x - 50 y = 75 \Rightarrow (3 \times 100) - 50 y = 75 \Rightarrow 300 - 50 y = 75 \Rightarrow - 50 y = - 225 \Rightarrow y = \frac{- 225}{- 50} ∴ y = 4.5 N o w p u t t i n g t h e v a l u e o f y i n (i i i) 3 x - 50 y = 75 \Rightarrow 3 x - (50) \times (4.5) = 75 \Rightarrow 3 x - 225 = 75 \Rightarrow 3 x = 225 + 75 \Rightarrow 3 x = 300 ∴ x = \frac{300}{3} = 100 ∴ T h e n u m b e r o f c h i l d r e n = 100 ∴ T h e t o t a l a m o u n t o f m o n e y d i s t r i b u t e d = x \times y = 4.5 \times 100 = 450 T k .$

ans: The number of children is 100 and amount of money 450 Tk.

16 views Answered 2024-12-14 13:31

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