problem from selection olympiad

For students of class 9-10 (age 14-16)
nimon
Posts:8
Joined:Sat Mar 27, 2021 7:30 am
problem from selection olympiad

Unread post by nimon » Fri Apr 02, 2021 11:47 am

এই প্রশ্ন টা কিভাবে সমাধান করছ ।
দুইটা একই উচ্চতার মোমবাতির একটা 9 ঘনটা অন্যটা 6 ঘন্টা জলে। রাতে মোমবাতি দুটো জালিয়ে ঘুমিয়ে গেলে।ঘুম থেকে উঠে দেখলে একটা মোমবাতির উচ্চতা অপরটির অর্ধেক। তুমি কতক্ষন ঘুমিয়েছ?

abidahsaf
Posts:4
Joined:Fri Aug 07, 2015 2:39 pm

Re: problem from selection olympiad

Unread post by abidahsaf » Sun Apr 04, 2021 11:36 am

Let us assume you were asleep for $t$ hours. The first candle loses $\frac{1}{9}$ part and the second candle loses $\frac{1}{6}$ part in 1 hour. So if you are asleep for $t$ hours, $1^{st}$ candle would have $$1-\frac{t}{9}$$ part remaining whereas the $2^{nd}$ candle will have $$1-\frac{t}{6}$$ part remaining when you wake up. Now, according to the question,

$1-\frac{t}{9} =2\left(1-\frac{t}{6}\right)$

Solving this equation, you will find $t=4.5$ hours.

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