Question

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एक समान लंबाई के दो मोमबत्ती हैं जिनको जलने पर क्रमसा: 5 घंटे or 4 घंटे में समाप्त हो जाती है माना प्रत्येक मोमबत्ती नियमित गति से जलती है मोमबत्ती के जलने के कितने समय बाद पहली और दूसरी मोमबत्ती का अनुपात 3:2 रह जाएंगे ?

There are two candles of the same length, which are finished in the sequence: 5 hours or 4 hours after burning: Each candle burns at regular speed. How many times after the candle burn, the ratio of first and second candles will remain at 3: 2?

☆ your options are ☆

(I) 3 hours
(II) 3:45
(III) 20/6
(Iv) Non of the above

Answer 1

I hope my answer is correct

The answer is d) none of the above

Because if we are doing with a) 3 hours then the answer is coming 5:4

If we are doing with b) 3:45 then the answer again is coming 5:4

And if we are doing with c) 20/6 then then the answer is coming 12:5

Therefore the answer is none of these

Thanks

Answer 2

Method - 1:

Let the candles be A and B.

(i) Given that Candle A takes 5 hours to burn, part of the candle burn in 1 hour = (1/5).

(ii) Given that Candle B takes 4 hours to burn, part of the candle burn in 1 hour = (1/4).

Let us assume that After 'x' hours the ratio of A and B will remain at 3:2

$= > \frac{1 - \frac{x}{5}}{1 - \frac{x}{4}} = \frac{3}{2}$

$= > 2 - \frac{2x}{5} = 3 - \frac{3x}{4}$

$= > 40 - 8x = 60 - 15x$

$= > -8x = -15x + 20$

$= > 7x = 20$

$= > x = \frac{20}{7}$

Therefore, the answer is 20/7 - Option(D)

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Method - 2:

Given that two candles are of same length.

Let their length (or) height be 'h'.

(i)

Given that first candle takes 5 hours to burn completely.

So, the first candle shortens by h/5 per hour.

(ii)

Given that second candle takes 4 hours to burn completely.

So, the second candle shortens h/4 per hour.

Now,

Let 'x' be time taken when ratio of first & second candles will remain 3:2.

So, in x hours:

⇒ Part of  first candle burns = hx/5.

⇒ Part of second candle burns = hx/4.

According to the given statement.

⇒ (h - hx/5)/(h - hx/4) = 3/2

⇒ h(1 - x/5)/h(1 - x/4) = 3/2

⇒ (1 - x/5)/(1 - x/4) = 3/2

⇒ 2 - 2x/5 = 3 - 3x/4

⇒ -8x = -15x + 20

⇒ 7x = 20.

⇒ x = 20/7.

Therefore, the answer is 20/7 -  Option (D)

Hope this helps!