Question

A ceiling fan was sold at a profit of 5%. Had it been sold for 50 more, the profit would have been 9%. Find the cost price of the ceiling fan

please tell fast ​

Answer 1

Step-by-step explanation:

Solution :-

Let the Cost Price of a ceiling fan be

Rs. X

Profit percentage on it = 5%

We know that

Selling Price = [(100+g)×CP]/100

=> SP = [(100+5)×X]/100

=> SP = 105X/100

=> SP = 21X/20

Therefore, Selling Price = Rs. 21X/20

If the ceiling fan sold for Rs. 50 more then the selling price will be (21X/20)+50

= Rs. (21X+1000)/20

Required Profit percentage = 9%

We know that

Selling Price = [(100+g)×CP]/100

=> (21X+1000)/20 = [(100+9)X]/100

=> (21X+1000)/20 = 109X/100

On applying cross multiplication then

=> 109X × 20 = (21X+1000)×100

=> 2180X = 2100X +100000

=> 2180X-2100X = 100000

=> 80X = 100000

=> X = 100000/80

=> X = 10000/8

=> X = 1250

Therefore, X = Rs. 1250

Answer :-

The Cost Price of the ceiling fan is

Rs. 1250

Check :-

The Cost Price of the ceiling fan is

Rs. 1250

Profit on it = 5%

Selling Price = [(100+5)×1250]/100

=> SP = (105×1250)/100

=> SP = 131250/100

=> SP = Rs. 1312.50

If the selling price is Rs. 50 more then it will be

= 1312.50+50 = Rs. 1362.50

Now,

Profit = Selling Price - Cost Price

=> Profit = 1362.50-1250

Therefore, Profit = Rs. 112.50

Profit% = (Profit /Cost Price)×100

=> Profit % = (112.50/1250)×100

=> Profit % = 11250/1250

=> Profit % = 1125/125

=> Profit% = 9%

Hence, Required Profit % = 9%

Verified the given relations in the given problem.

Used formulae:-

→ Selling Price = [(100+g)×CP]/100

→ Profit = Selling Price - Cost Price

→ Profit% = (Profit /Cost Price)×100

Answer 2

$\large \underline{\underline{\rm{ \bull \: Information \: mentioned \: in \: question: - }}}$

➻ A ceiling fan was sold at a profit of 5%.

➻ Had it been sold for 50 more, the profit would have been 9%.

$\overline{\rule{ 200pt}{2pt}}$

$\large \underline{\underline{\rm{ \bull \: What \: we \: have \: To \: Find \: out : - }}}$

➻ The cost price of selling fan

$\large \underline{\underline{\rm{ \bull \:Which \: Formula \: we \: have \: to \: Used : - }}}$

${\underline{\boxed{\red{\sf{ S.P= \bigg\lgroup 1 + \dfrac{p}{100} \bigg\rgroup \:of \: C.P }}}}}$

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

$\qquad{ ━━━━━━━━━━━━━━━━━━━━━━━━━━━}$

Where :

➻ S.P = Selling Price

➻ p = Profit

➻ C.P= Cost Price

$\qquad{ ━━━━━━━━━━━━━━━━━━━━━━━━━━━}$

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

$\large \underline{\underline{\rm{ \bull \:Assume \: that : - }}}$

➳ The cost price of ceiling fan let be Rs x.

$\large \underline{\underline{\rm{ \bull \:We \: know \: that : - }}}$

➻ Profit = 5 percent

$\large \underline{\underline{\rm{ \bull \:Now \: By \: using \: formula : - }}}$

$\dag \underline{ \boxed{ \sf{S.P= \bigg \lgroup 1 + \dfrac{p}{100} \bigg \rgroup \: of \: C.P }}}$

$\large \underline{\underline{\rm{ \bull \: By \: putting \: value : - }}}$

$\sf{ \: \mapsto \: S.P=\bigg\{1 \pmb{+} \dfrac{5}{100} \bigg \}} \: of \: Rs \: x$

$\sf{\: \mapsto \: \bigg\{ \dfrac{105}{100} \bigg \}} \: of \: Rs \: x = \: Rs \: \dfrac{105}{100} \: x$

$\large \underline{\underline{\rm{ \bull \: Similarly : - }}}$

➻ To obtain 9 percent profit

$\sf{\: \mapsto \: S.P=\bigg\{1 \pmb{+} \dfrac{9}{100} \bigg \}} \: of \: Rs \: x$

$\sf{\: \mapsto \: \bigg\{ \dfrac{109}{100} \bigg \}} \: of \: Rs \: x = \: Rs \: \dfrac{109}{100} \: x$

$\large \underline{\underline{\rm{ \bull \: Now : - }}}$

➻ According to given information ,

$\rm \implies \: { \dfrac{109}{100} \: x = \dfrac{105}{100} + 50 }$

$\large \underline{\underline{\rm{ \bull \: Calculation : - }}}$

$\rm \implies{ \dfrac{105 \: x}{100} + 50 = \dfrac{109}{100} } \: x$

$\rm \implies{50 = \dfrac{109}{100} \: x- \dfrac{105 \: x}{100}}$

$\rm \implies{50 = (\dfrac{109}{100} \: - \dfrac{105}{100}) \: x}$

$\rm \implies{50 = (\dfrac{109 - 105}{100} ) \: x}$

$\rm \implies{50 = (\dfrac{4}{100} ) \: x}$

$\rm \implies{50 = (\dfrac{4 \: x}{100}})$

$\rm \implies{50 = (\dfrac{ \: x}{25}})$

$\rm \implies{x = 50 \times 25}$

$\implies \dag \underline{ \boxed{ \rm{ x = Rs \: 1,250 }}}$

$\large \underline{\underline{\rm{ \bull \: Therefore : - }}}$

• ➻ ❛❛ Cost of the selling fan is 1.250 Rs . ❜❜

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