Question

A Nokia phone and Glo-sim where sold for #3,040 making a profit of 25% on the phone & 10% on the SIM card. By selling them for #3,070, the profit realized would have been 10% on the phone and 25% on the SIM. Find the cost price of each.

Answer 1

AnswEr :

Let the Cost Price of Phone be x and, Cost Price of Sim Card be y.

$\bf{ Given}\begin{cases}\sf{Profit \:on \:Phone = 25\%}\\\sf{Profit \:on \:Sim \:Card = 10\%}\\ \sf{SP = Rs. \: 3040}\end{cases}$

• According to the 1st Part of Question :

$\longrightarrow \tt SP \:of \:Phone + SP \:of \:Sim \:Card = Total \:SP \\ \\\longrightarrow \tt CP_{Phone} \times (100 + Profit)\% + CP_{Sim \:Card} \times (100 + Profit)\% = 3040 \\ \\\longrightarrow \tt x\times (100 + 25)\% + y\times (100 + 10)\% = 3040 \\ \\\longrightarrow \tt (x \times 125\%) + (y \times 110\%) = 3040 \\ \\\longrightarrow \tt x \times \dfrac{125}{100} + y \times \dfrac{110}{100} = 3040 \\ \\\longrightarrow \tt \dfrac{125x}{100} + \dfrac{110y}{100} = 3040 \\ \\\longrightarrow \tt \dfrac{125x + 110y}{100} = 3040 \\ \\\longrightarrow \red{\tt125x + 110y = 304000}\qquad\dfrac{ \quad}{}eq.(1)$

$\rule{200}{1}$

$\bf{ Given}\begin{cases}\sf{Profit \:on \:Phone = 10\%}\\\sf{Profit \:on \:Sim \:Card = 25\%}\\ \sf{SP = Rs. \: 3070}\end{cases}$

• According to the 2nd Part of Question :

$\longrightarrow \tt SP \:of \:Phone + SP \:of \:Sim \:Card = Total \:SP \\ \\\longrightarrow \tt CP_{Phone} \times (100 + Profit)\% + CP_{Sim \:Card} \times (100 + Profit)\% = 3070 \\ \\\longrightarrow \tt x\times (100 + 10)\% + y\times (100 +25)\% = 3070 \\ \\\longrightarrow \tt (x \times 110\%) + (y \times 125\%) = 3070 \\ \\\longrightarrow \tt x \times \dfrac{110}{100} + y \times \dfrac{125}{100} = 3070 \\ \\\longrightarrow \tt \dfrac{110x}{100} + \dfrac{125y}{100} = 3070 \\ \\\longrightarrow \tt \dfrac{110x + 125y}{100} = 3070 \\ \\\longrightarrow \red{\tt110x + 125y = 307000}\qquad\dfrac{ \quad}{}eq.(2)$

$\rule{200}{2}$

• Multiplying eq.(1) by 110 and, eq.(2) by 125 and subtracting it :

$\implies \tt 13750x + 15625y = 38375000\\\\\implies \tt 13750x + 12100y = 33440000 \\\dfrac{ \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad}{}\\\implies \tt 3525y = 4935000 \\ \\\implies \tt y = \cancel\dfrac{4935000}{3525} \\ \\\implies \tt y= Rs. \:1400$

$\rule{100}{2}$

• Putting the value of y in eq.( 1) :

↠ 125x + 110y = 304000

↠ 125x + 110(1400) = 304000

↠ 125x + 154000 = 304000

↠ 125x = 304000 – 154000

↠ 125x = 150000

• Dividing both term by 125

↠ x = Rs. 1200

⠀

∴ Cost Price of Phone and Sim Card is Rs. 1200 and Rs. 1400 respectively.

Answer 2

Given :--

• when nokia is sold at 25% profit and gio-sim is sold at 10% profit total SP will be Rs.3040.
• when nokia is sold at 10% profit and gio-sim is sold at 25% profit total SP will be Rs.3070.

Solution :--

Let, CP of Nokia Phone is = x

→ Let CP of gio-sim = y

Now, To make calculation Easy, lets change given % into Fraction ,

→ 25% Profit = 125% = 125/100 = 5/4

→ 10% Profit = 110% = 110/100 = 11/10 .

So, From First case Now, we can say That :---

→ 5x/4x + 11y/10 = 3040

→ 25x + 22y = 60800 ------------- Equation (1)

Now, From Case 2 we get,,

→ 11x/10 + 5y/4 = 3070

→ 22x + 25y = 61400 -------------- Equation (2)

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Now, Multiply Equation (1) by 22 and Equation (2) by 25 and Than subtracting Equation (1) From Equation (2) we get,,

→ 25(22x+25y) - 22(25x+22y) = 25(61400) - 22(60800)

→ 550x + 625y - 550x - 484y = 197400

→ 141y = 197400

→ y = 197400/141

→ y = Rs.1400

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Putting value of y now in Any Equation we can easily Find value of x .

→ 25x +22*1400 = 60800

→ 25x = 60800 - 30800

→ 25x = 30000

→ x = Rs.1200

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Hence, we The Cost Price of Nokia Phone is Rs.1200 and Cost Price of Gio-Sim is Rs.1400 ..

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★★Extra Brainly Knowledge★★

→ CP + Profit = SP

→ CP - Loss = SP

→ Profit/Loss% = (ProFit/Loss in Rs.)*100/CP .

→ SP = CP*(100±P% or L%)/100 ( where + is if Profit % and - is if Loss%)

→ CP = SP*100/(100±P% or L%)