Question

The cost of an object is increased by 20%. If the current cost is ₹ 600, what was its original cost?

Answer 1

Solution :

The cost of an object is increased by 20% and after that, it's current cost is Rs. 600

We have to find it's original cost.

Suppose it's original cost is Rs. x

After it being increased by 20%

New cost :

>> 120% of x

This is equal to 600

>> 120% of x = 600

>> (120/100)x = 600

>> x/100 = 5

>> x = Rs. 500

It's original cost is Rs. 500

$\boxed{\begin{minipage}{5cm}\bigstar \:\underline{\textbf{Profit and Loss Formulas :}}\\\\ \\ \sf {\textcircled{\footnotesize\textsf{1}}} \:S.P. = \sf \bigg\lgroup\dfrac{100 + Profit \%}{100}\bigg\rgroup \times \: C.P. \\\\\\ \sf {\textcircled{\footnotesize\textsf{2}}} \:\:C.P. = \sf \dfrac{S.P. \times 100}{100 + Profit \%} \\\\\\\sf{\textcircled{\footnotesize\textsf{3}}} \:\:Profit = \sf \dfrac{Profit \% \times C.P.}{100} \\\\\\ \sf{\textcircled{\footnotesize\textsf{4}}} \: \:Profit (gain) = S.P. - C.P. \\\\\\\sf{\textcircled{\footnotesize\textsf{5}}} \: \: \sf Profit \% = \dfrac{Profit}{C.P.} \times 100 \end{minipage}}$

Answer 2

Given :

• New price = Rs.600
• Increase % = 20 %

$\\ \rule{200pt}{3pt}$

To Find :

• Old price = ?

$\\ \rule{200pt}{3pt}$

Solution :

✭ ${\underline{\pmb{\frak{ Formula \; Used \; :- }}}}$

• ${\underline{\boxed{\purple{\sf{ New \; Price = \bigg\lgroup \dfrac{100 + Increase \; \% }{100} \bigg\rgroup \times Old \; Price }}}}}$

$\\ \qquad{\rule{150pt}{1pt}}$

✭ ${\underline{\pmb{\frak{ Calculating \; the \; Old \; Price \; :- }}}}$

$\begin{gathered} \dashrightarrow \; \; \sf { New \; Price = \bigg\lgroup \dfrac{100 + Increase \; \% }{100} \bigg\rgroup \times Old \; Price } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { 600 = \bigg\lgroup \dfrac{100 + 20 }{100} \bigg\rgroup \times Old \; Price } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { 600 = \bigg\lgroup \dfrac{120}{100} \bigg\rgroup \times Old \; Price } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { 600 \times 100 = 120 \times Old \; Price } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { 60000 = 120 \times Old \; Price } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { \dfrac{60000}{120} = Old \; Price } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { \cancel\dfrac{60000}{120} = Old \; Price } \\ \end{gathered}$

${\qquad \; \; {\therefore \; {\underline{\boxed{\red{\pmb{\frak{ Old \; Price = ₹ \; 500 }}}}}}}}$

$\\ \qquad{\rule{150pt}{1pt}}$

✭ ${\underline{\pmb{\frak{ Therefore \; :- }}}}$

❛❛ Old price of the object was ₹ 500 . ❜❜

$\\ {\underline{\rule{300pt}{9pt}}}$