Solve the following Mathematical Problems

Two candles having the same length are such that one burns out completely in 3 hours at a uniform rate and the other in 4 hours. At what time should both the candles be lighted together so that at 4 PM, the length of one is twice the length of the other?

Created: 1 year ago | Updated: 1 year ago

Updated: 1 year ago

প্রশ্নে বলা হচ্ছে যে, দুটি মোমবাতি একটি সুষম গতিতে 3 ঘণ্টায় ও অপরটি ও 4 ঘণ্টা পুরোপুরি জ্বলে শেষ হয়। কখন দুটি মোম একত্রে জ্বালালে বিকাল 4 টার সময় একটির দৈর্ঘ্য অপরটির দ্বিগুণ থাকবে?

$L e t l b e l e n g t h o f e a c h c a n d l e a n d x b e t h e n u m b e r o f h o u r s b e f o r e 4 p m . ∴ L e n g t h o f 1^{s t} c a n d l e b u r n t (\frac{1}{3}) x ∴ L e n g t h o f 2^{n d} c a n d l e b u r n t (\frac{1}{4}) x ∴ R e m a i n i n g o f 1^{s t} c a n d l e = (l - \frac{l x}{3}) a t 4 p m & R e m a i n i n g o f 2^{n d} c a n d l e = (l - \frac{l x}{4}) a t 4 p m A c c o r d i n g t o q u e s t i o n, l - \frac{l x}{4} = 2 (l - \frac{l x}{3}) \Rightarrow l (1 - \frac{x}{4}) = 2 l (1 - \frac{x}{3}) \Rightarrow 1 - \frac{x}{4} = 2 (1 - \frac{x}{3}) \Rightarrow 1 - \frac{x}{4} = 2 - \frac{2 x}{3} \Rightarrow \frac{2 x}{3} - \frac{x}{4} = 2 - 1 \Rightarrow \frac{4 x - 3 x}{12} = 1 \Rightarrow \frac{5 x}{12} = 1 ∴ x = \frac{12}{5} = 2 \frac{2}{5} h o u r s = 2 h o u r s a n d 24 m i n u t e s ∴ R e q u i r e d t i m e s = 4 - 2 h o u r s 24 m i n u t e s = 1 h o u r 36 m i n u t e s = 1 : 36 p m$