Question

On Diwali eve, two candles, one of which is 3 cm longer than the other are

lighted. The longer one is lighted at 5.30 p.m. and the shorter at 7 p.m. At

9.30p.m. they both are of the same length. The longer one burns out at

11.30p.m. and the shorter one at 11 p.m. How long was each candle

originally?

​

Answer 1

Answer:

x and x + 3 are the lengths

x + 3 was lit at 3:30

at 7:30, it was the same length as the other candle (4 hours)

(x + 3) - 4 * k = x - 2.5 * m

After 6 hours, the longer candle burned out

x + 3 - 6k = 0

After 4 hours, the shorter candle burned out

x - 4m = 0

x + 3 = 6k

k = (x + 3) / 6

x - 4m = 0

x = 4m

x/4 = m

(x + 3) - 4 * k = x - 2.5 * m

(x + 3) - 4 * (x + 3) / 6 = x - (5/2) * (x/4)

(x + 3) * (1 - 2/3) = x * (1 - 5/8)

(x + 3) * (1/3) = x * (3/8)

x/3 + 1 = 3x/8

1 = 3x/8 - x/3

1 = 9x/24 - 8x/24

1 = x/24

24 = x

24 cm and 27 cm

Answer 2

• The length of longer candle originally was 27 m and the length of shorter candle originally was 24 m .

Given :-

• One candle was 3 cm longer than the other .
• The longer one is lighted at 5.30 p.m. and the shorter at 7 p.m.
• At 9.30p.m. they both are of the same length.
• The longer one burns out at 11.30p.m. and the shorter one at 11 p.m.

To Find :- How long was each candle originally ?

Solution :-

Let us assume that, the longer candle burns at the rate of x m / hour and the shorter candle burns at the rate of y m / hour .

so,

→ Longer candle buring rate = x m / hour

→ Total time taken by longer candle to burn completely = 11:30PM - 5:30PM = 6 hours

then,

→ Total length of longer candle = Burning rate × Total time taken = x × 6 = 6x m ---- Equation (1)

similarly,

→ Shorter candle buring rate = y m / hour

→ Total time taken by shorter candle to burn completely = 11 PM - 7 PM = 4 hours

then,

→ Total length of shorter candle = Burning rate × Total time taken = y × 4 = 4y m ---- Equation (2)

Now, we have given that, longer candle is 3 m longer than the shorter candle . Subtracting Equation (2) from Equation (1) we get,

→ 6x - 4y = 3 --------- Equation (3)

Now, we have given that, at 9.30PM they both are of the same length .

So,

→ Length of longer candle burns upto 9:30 PM = Total time × Rate = (9:30PM - 5:30PM) × x = 4x m

then,

→ Total length of longer candle at 9:30PM = Total length - Length burns = 6x - 4x = 2x m ---- Equation (4)

similarly,

→ Length of shorter candle burns upto 9:30 PM = Total time × Rate = (9:30PM - 7PM) × y = 2:30 × y = 2.5 × y = 2.5y m

then,

→ Total length of shorter candle at 9:30PM = Total length - Length burns = 4y - 2.5y = 1.5y m ---- Equation (5)

putting Equation (4) and Equation (5) equal now,

→ 2x = 1.5y

→ 2x = (3y/2)

→ x = (3y/4)

putting value of x in Equation (3),

→ 6x - 4y = 3

→ 6(3y/4) - 4y = 3

→ (18y/4) - 4y = 3

→ (18y - 4×4y)/4 = 3

→ (18y - 16y) = 3 × 4

→ 2y = 12

→ y = 6 m / hour

putting value of y now,

→ x = (3y/4)

→ x = (3 × 6)/4

→ x = 4.5 m / hour

therefore, putting value in x in Equation (1) we get,

→ Total length of longer candle = 6x = 6 × 4.5 = 27 m (Ans.)

and, putting value in y in Equation (2) we get,

→ Total length of shorter candle = 4y = 4 × 6 = 24 m (Ans.)

Hence, length of longer and shorter candle are 27 m and 24 m respectively .

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