Question

Rani ate 2/7 part of a cake while her brother ravi ate 4/5 of the remaining. part of the cake left is?​

Answer 1

QUESTION:-

• rani ate 2/7 part of a cake while her brother ravi ate 4/5 of the remaining. Find the part of the cake left is?

Given:-

• Rani ate cake = $\sf\green{ \frac{2}{7} }$
• Ravi ate cake = $\sf\green{ \frac{4}{5} }$

To Find:-

• Left over part of cake

Solution:-

$\boxed{ \sf \blue{ Now, \: let \: us\: assume\: total\: part \: of \: cake \: be \: 1.}}$

For Rani :-

• $\frac{2}{7}$part of a cake

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\: 1 \: - \: \frac{2}{7} }} }\\ \\\end{gathered}\end{gathered}$

$\sf\red{ Make \: the \: bases \: same \: by \: taking \: their \: LCM }$

$\begin{gathered}\begin{gathered}: \implies \displaystyle \sf \: \frac{7 \: - \: 2}{7} \\ \\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \displaystyle \sf \: \frac{5}{7} \\ \\ \\\end{gathered}\end{gathered}$

For Ravi :-

• $\frac{4}{5}$part of a cake

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\: \frac{4}{5} \: \times \: \frac{5}{7} }} }\\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \displaystyle \sf \: \frac{4}{7} \\ \\ \\\end{gathered}\end{gathered}$

Remaining cake :-

$\boxed{ \sf \green{ Rani \: part \: - \: Ravi \: part \: = \: Total \: Cake}}$

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\: \frac{2}{7} \: - \: \frac{4}{7} }} }\\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\: \frac{1}{7} }} }\\ \\\end{gathered}\end{gathered}$

$\boxed{ \sf \blue{ So, \: \frac{1}{7} \: part \: was \: left \: in \: the \: cake }}$