Question

find the number whose half part increased by 30 is equal to its fourth part decreased by 30​

Answer 1

Solution==>
Let the number =>x
A.T.Q=>
-------
It's half part=x/2
and,it's fourth part=x/4
Now, According to question.,
half part is increased by 30=fourth part is decreased by 30
Therefore,
$\frac{x}{2} + 30 = \frac{x}{4} = - 30 \\ \\ \frac{x}{4} - \frac{x}{2} = - 30 - 30 \\ \\ by \: taking \: lcm \: on \: left \: hand \: side \\ \\ \frac{ - 2x}{4} = - 60 \\ \\ - 2x = - 240 \\ x = \frac{ - 240}{ - 2 } \\ x = 120$
Therefore, the number is 120

Answer 2

Answer:

Solution==>

Let the number =>x

A.T.Q=>

-------

It's half part=x/2

and,it's fourth part=x/4

Now, According to question.,

half part is increased by 30=fourth part is decreased by 30

Therefore,

\begin{gathered} \frac{x}{2} + 30 = \frac{x}{4} = - 30 \\ \\ \frac{x}{4} - \frac{x}{2} = - 30 - 30 \\ \\ by \: taking \: lcm \: on \: left \: hand \: side \\ \\ \frac{ - 2x}{4} = - 60 \\ \\ - 2x = - 240 \\ x = \frac{ - 240}{ - 2 } \\ x = 120\end{gathered}

2

x

+30=

4

x

=−30

4

x

−

2

x

=−30−30

bytakinglcmonlefthandside

4

−2x

=−60

−2x=−240

x=

−2

−240

x=120