Question

Rupa lit 15 candles in $2\dfrac{1}{4}$ minutes. How many seconds did she take? How many candles can she light in $4\dfrac{1}{2}$ minutes?

Answer 1

Hint: To obtain the value of second taken by Rupa to light 15 candles we will use the conversion value of minute to second. Firstly we will convert the mixed number into fraction and then convert the minute taken by Rupa in seconds. Then we will find the number of candles lit by her in 1 minute and then multiply it by the given minute to get our desired answer.

Complete step by step answer:
It is given to us that Rupa lit 15 candles in $2\dfrac{1}{4}$ minutes so we can write it as,
In $2\dfrac{1}{4}\min =15$ Candles
$\dfrac{9}{4}\min =15$ Candles……$\left( 1 \right)$
So as we have to find the value in seconds we know that:
$1\min =60$ Seconds
So $\dfrac{9}{4}$ minute will be equal to:
$\begin{align}
  & \Rightarrow \dfrac{9}{4}\times 60 \\
 & \Rightarrow 9\times 15 \\
 & \Rightarrow 135 \\
\end{align}$
So $\dfrac{9}{4}$ minute is equal to 135 seconds.
Next we have to find how many candles she can light in $4\dfrac{1}{2}$ minutes.
From equation (1) we have:
In $\dfrac{9}{4}\min =15$ Candles
$\begin{align}
  & 1\min =\dfrac{15}{\left( \dfrac{9}{4} \right)} \\
 & 1\min =\dfrac{15\times 4}{9} \\
 & 1\min =\dfrac{5\times 4}{3} \\
 & 1\min =\dfrac{20}{3} \\
\end{align}$
So we got,
In $1\min =\dfrac{20}{3}$ Candles
In $4\dfrac{1}{2}\min =\dfrac{20}{3}\times 4\dfrac{1}{2}$
$\begin{align}
  & 4\dfrac{1}{2}\min =\dfrac{20}{3}\times \dfrac{9}{2} \\
 & 4\dfrac{1}{2}\min =10\times 3 \\
\end{align}$
$4\dfrac{1}{2}\min =30$ Candles
So Rupa lights 30 candles in $4\dfrac{1}{2}$ minutes.
Hence Rupa took 135 seconds to light 15 candles and she can light 30 candles in $4\dfrac{1}{2}$ minutes.

Note: Mixed numbers is the combination of whole numbers and proper fractions represented together. That is the reason a mixed number has partial properties of a whole number and partial property of a fraction. In general it represents a number between any two whole numbers. While doing the calculation we should always change the mixed number into fraction as it makes the calculation less complicated.