There are two candles of the same length and | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the initial length of both candles be $L$.The rate of burning for the first candle is $\frac{L}{5}$ per hour,and for the second candle is $\fr

Vedclass · Accepted Answer

$150$

Vedclass · Answer

(D) Let the initial length of both candles be $L$.The rate of burning for the first candle is $\frac{L}{5}$ per hour,and for the second candle is $\frac{L}{3}$ per hour.Let $t$ be the time in hours after which the length of the first candle is $3$ times the length of the second candle.The remaining lengths after time $t$ are $L_1 = L - \frac{L}{5}t$ and $L_2 = L - \frac{L}{3}t$.According to the problem,$L_1 = 3L_2$.Substituting the expressions: $L - \frac{L}{5}t = 3(L - \frac{L}{3}t)$.Dividing by $L$: $1 - \frac{t}{5} = 3 - t$.Rearranging the terms: $t - \frac{t}{5} = 3 - 1$.$\frac{4t}{5} = 2$.$t = \frac{10}{4} = 2.5 \, hr$.Converting to minutes: $2.5 	imes 60 = 150 \, min$.

There are two candles of the same length and size. Both of them burn at a uniform rate. The first one burns in $5 \, hr$ and the second one burns in $3 \, hr$. Both the candles are lit together. After how many minutes is the length of the first candle $3$ times that of the other?

Similar Questions

The locus of the midpoint of the portion of the line $x \cos \alpha + y \sin \alpha = p$ intercepted by the coordinate axes,where $p$ is a constant,is

Let $A(5, -3)$,$B(3, -2)$,and $C(-1, 5)$ be three points. If $P$ is a point satisfying the condition $PA^2 + 2PB^2 = 3PC^2$,then a point that lies on the locus of $P$ is

$A$ straight line $L$ cuts both the lines $5x - y - 4 = 0$ and $3x + 4y - 4 = 0$. The segment of $L$ between the two lines is bisected at the point $(1, 5)$. The equation of $L$ is

$A$ quadrilateral $ABCD$ is divided by the diagonal $AC$ into two triangles of equal areas. If $A, B, C$ are respectively $(3, 4), (-3, 6), (-5, 1)$,then the locus of $D$ is

If $a, b, c$ are in Arithmetic Progression $(AP)$,then the line $ax + by + c = 0$ always passes through a fixed point. The coordinates of this point are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module