Question

Anu earns a profit or 18% by selling an article at a certain price. If she were to sell it for 10.50 more, she would have gained 25%. The original cost price of 12 such
articles is​

Answer 1

Answer:

Let:−

\tt{\leadsto Cost\: price\:_{(article)}=x}⇝Costprice(article)=x

\sf\small\underline\purple{To\:Find:-}ToFind:−

\tt{\leadsto Cost\: price\:_{(12\:article)}=?}⇝Costprice(12article)=?

\sf\small\underline\purple{Solution:-}Solution:−

We will solve this question by applying formula. As per the given clue in the question.

\sf\small\underline\pink{Given\:in\:case-(i):-}Givenincase−(i):−

\tt\small\underline{CP=x\:\:\:P=18\%:-}CP=xP=18%:−

\tt{\leadsto SP=\bigg(\dfrac{100+P\%}{100}\bigg)\times\:CP}⇝SP=(100100+P%)×CP

\tt{\leadsto SP=\bigg(\dfrac{100+18}{100}\bigg)\times\:x}⇝SP=(100100+18)×x

\tt{\leadsto SP=\bigg(\dfrac{118}{100}\bigg)\times\:x}⇝SP=(100118)×x

\tt{\leadsto SP=\bigg(\dfrac{118x}{100}\bigg)}⇝SP=(100118x)

\tt{\leadsto SP=\dfrac{118x}{100}+10.50}⇝SP=100118x+10.50

\sf\small\underline\pink{Given\:in\:case-(ii):-}Givenincase−(ii):−

\tt\small\underline{CP=x\:\:\:P=25\%:-}CP=xP=25%:−

\tt{\leadsto SP=\bigg(\dfrac{100+P\%}{100}\bigg)\times\:CP}⇝SP=(100100+P%)×CP

\tt{\leadsto SP=\bigg(\dfrac{100+25}{100}\bigg)\times\:x}⇝SP=(100100+25)×x

\tt{\leadsto SP=\bigg(\dfrac{125}{100}\bigg)\times\:x}⇝SP=(100125)×x

\tt{\leadsto SP=\bigg(\dfrac{125x}{100}\bigg)}⇝SP=(100125x)

\tt{\leadsto SP=\dfrac{125x}{100}}⇝SP=100125x

\sf{Cp\:of\: orginal\: article:-}Cpoforginalarticle:−

\tt{\leadsto SP\:_{(case-(ii))}=SP\:_{(case-(i))}}⇝SP(case−(ii))=SP(case−(i))

\tt{\leadsto \dfrac{125x}{100}=\dfrac{118x}{100}+10.50}⇝100125x=100118x+10.50

\tt{\leadsto \dfrac{125x}{100}-\dfrac{118x}{100}=10.50}⇝100125x−100118x=10.50

\tt{\leadsto \dfrac{125x-118x}{100}=10.50}⇝100125x−118x=10.50

\tt{\leadsto \dfrac{7x}{100}=10.50}⇝1007x=10.50

\tt{\leadsto 7x=1050}⇝7x=1050

\tt{\leadsto x=150}⇝x=150

\sf\large{Hence,}Hence,

\tt{\leadsto Cost\: price\:_{(12\:article)}=12x}⇝Costprice(12article)=12x

\tt{\leadsto Cost\: price\:_{(12\:article)}=12(150)}⇝Costprice(1800

Step-by-step explanation:

hope it helps!!

Answer 2

Answer:

Original cost price is 150

Step-by-step explanation:

Let original cost be x

$S.P.= x + \dfrac{18}{100}x= \dfrac{118}{100}x$     equation (1)

If the selling price increases by 10.5, then profit is of 25%, So,

$S.P.+10.5=\dfrac{125}{100}x$      equation(2)

Using (1) in (2)

$\dfrac{118}{100}x +10.5 = \dfrac{125}{100}x\\\\\rightarrow x=150$

Cost price is 150