The Candle Light Study

Power went off when Vipul was studying. It was around 2:00 AM. He lighted two uniform candles of equal length but one thicker than the other. The thick candle is supposed to last four hours and the thin one one hours less. When he finally went to sleep, the thick candle was twice as long as the thin one.

For how long did Vipul study in candle light?

Well, he studied in candle light for....hours. Know here! 

The Candle Light Studying Hours

What was the question?

It's clear that, the thick candle lasts for 4 hours and thin one lasts only 3 hours.

If L is length of these candles (they are of equal length) then thick candle burns L/4 per hour and thin one burns L/3 per hour.

Let's assume Vipul studied for X hours.

In X hours, amount of thick candle burnt = XL/4

 

In X hours, amount of thin candle burnt = XL/3

 

After X hours, amount of thick candle remaining = L - XL/4

 

After X hours, amount of thin candle remaining = L - XL/3

 

Also, it is given that the thick candle was twice as long as the thin one when he finally went to sleep.

 

(L - XL/4) = 2(L - XL/3 )

 

L(1 - X/4) = 2L (1 - X/3)

(1 - X/4) = 2(1 - X/3)

 

(4 - X)/4 = 2(3 - X)/3

3(4 - X) = 8(3 - X)

12 - 3X = 24 - 8X

5X = 12

X=12/5

 

Converting 12/5 hours into minutes as X = 12/5 * 60 = 144 minutes.

 

Hence, Vipul must have studied for 2 hours and 24 minutes.

 

 

  

Lighting Up The Candles

In a group of 200 people, everybody has a non burning candle. On person has a match at lights at some moment his candle. With this candle he walks to somebody else and lights a new candle. Then everybody with a burning candle will look for somebody without a burning candle, and if found they will light it. This will continue until all candles are lit. Suppose that from the moment a candle is lit it takes exactly 30 seconds to find a person with a non burning candle and light that candle.

From the moment the first candle is lit, how long does it take before all candles are lit?

ESCAPE to answer! 

Time Calculation For Lighting Up The Candles

What is the exact situation?

From a moment from first candle is lit, 30 seconds later there would be total 2 candles lit. In next 30 seconds, each of these 2 candle holders will find 1 candle to lit. So there are now 4 candles lit after 60 seconds. In next 30 seconds, these 4 candles would lit another 4 candles making total 8 candles lit. 

In short, for every 30 seconds, the number of candles lit are doubled. So after 7 sets of 30 seconds, 2^7 = 128 candles would be lit. At 8th set of 30 seconds, 256 candles can be lit. But we have only 200 candles. Still 72 of 128 candles would lit another 72 in 8th set of 30 seconds. 

To conclude, 8 X 30 = 240 seconds = 4 minutes required to lit all 200 candles. 

The Wisest Son Deserves Rewards

What was the condition? 

The third son was very wise to choose his option (like you did while choosing to read this blog). There are two/three possible things that he might have bought.

1. He bought a candle & match box. Just ignited that candle in room & light filled in entire room.

2. He just bought perfume & sprayed in room. The smell of perfume occupied the entire room.