solve the following mathematical problem:

A family has 480kg of rice for X number of weeks. If they need to use the same amount for 4 more weeks, they need to cut down their weekly assumption of rice by 4kg. What is the value of X?

Created: 1 year ago | Updated: 1 year ago

Updated: 1 year ago

প্রশ্নে বলা হচ্ছে, X সপ্তাহের জন্য একটি পরিবারের নিকট 480kg চাল রয়েছে। তারা যদি ঐ চাল আরো 4 সপ্তাহ চালাতে চায়, তবে তাদের সাপ্তাহিক চালের ভোগের পরিমাণ 4kg কমাতে হবে। X এর মান কত?

Here, X is the number of weeks.

The amount of rice is 480kg.

∴ If they need to run 4 more weeks, they need to imply following equation.

$\frac{480}{x} - \frac{480}{(x + 4)} = 4 \Rightarrow 480 (\frac{1}{x} - \frac{1}{(x + 4)}) = 4 \Rightarrow \frac{1}{x} - \frac{1}{(x + 4)} = \frac{4}{480} = \frac{1}{120} \Rightarrow \frac{x + 4 - x}{x (x + 4)} = \frac{1}{120} \Rightarrow \frac{4}{x^{2} + 4 x} = \frac{1}{120} \Rightarrow x^{2} + 4 x = 480 \Rightarrow x^{2} + 4 x - 480 = 0 \Rightarrow x^{2} + 24 x - 20 x - 480 = 0 \Rightarrow x (x + 24) - 20 (x + 24) = 0 \Rightarrow (x + 24) (x - 20) = 0 H e r e, x - 20 = 0 ∴ x = 20 B u t, x = - 24 i s n o t a c c e p t a b l e . ∴ T h e v a l u e o f x i s 20 .$