Question

A dealer sold a suitcase and an airbag for Rs.1884 by making a profit of 10% on suitcase and 12% on airbag. By selling them for Rs.1890, he would have made a profit of 12% on the suitcase and 10% in airbags. Find the cost price of each.

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Answer 1

$\huge{\underline{\purple{\rm{Solution:}}}}$

$\small{\underline{\green{\rm{Given\:in\:case\:1:}}}}$

$\sf{The\: selling\: price\: suitcase\:and\: airbag=1884}$

$\sf{Profit\:on\: suitcase=10\%}$

$\sf{Profit\:on\: airbag=12\%}$

$\bold\green{\underline{Let:}}$

$\sf{The\:cost\:price\:of\: suitcase\:be\:X}$

$\sf{The\:cost\:price\:of\: airbag\:be\:y}$

$\small{\underline{\red{\rm{A.T.Q:}}}}$

• Using formula here

$\small{\boxed{\green{\rm{SP=(\frac{100+G\%}{100})*CP:}}}}$

$\sf{\longrightarrow \frac{110}{100}*x+\frac{112}{100}*y=1884}$

$\sf{\longrightarrow 1.10x+1.12y=1884-----(i)}$

$\small{\underline{\red{\rm{Given\:in\:2nd\:case:}}}}$

$\sf{The\: selling\: price\: suitcase\:and\: airbag=1890}$

$\sf{Profit\:on\: suitcase=12\%}$

$\sf{Profit\:on\: airbag=10\%}$

• Now solving similarly,

$\sf{\longrightarrow \frac{112}{100}*x+\frac{110}{100}*y=1890}$

$\sf{\longrightarrow 1.12x+1.10y=1890-----(ii)}$

• Now, Solving equation 1 and 2

$\sf{\longrightarrow 1.10x+1.12y=1884}$

$\sf{\longrightarrow 1.12x+1.10y=1890}$

$\sf{\longrightarrow 1.232x+1.2544y=2110.08}$

$\sf{\longrightarrow 1.232x+1.21y=2079}$

$\sf{\longrightarrow 0.0444y=31.08}$

$\sf{\longrightarrow y=700}$

• Putting the value of y=700 in EQ 1

$\sf{\longrightarrow 1.10x+1.12y=1884}$

$\sf{\longrightarrow 1.10x+1.12*700=1884}$

$\sf{\longrightarrow 1.10x+784=1884}$

$\sf{\longrightarrow 1.10x=1884-784}$

$\sf{\longrightarrow 1.10x=1100}$

$\sf{\longrightarrow x=1000}$

Hence,

$\small{\boxed{\red{\rm{The\:cost\:price\:of\: suitcase=1000}}}}$

$\small{\boxed{\green{\rm{The\:cost\:price\:of\: airbag=700}}}}$

Answer 2

Given :-

• 10% Profit on Suitcase + 12% profit airbag = Rs.1884
• 12% Profit on Suitcase + 10% profit airbag = Rs.1890

Solution :-

Let cost Price of suitcase if S and cost Price of airbag is A .

Case 1 :-

→ (S + 10% of S) + (A + 12% of A) = 1884

→ S(1 + 10%) + A(1 + 12%) = 1884

→ 1.1S + 1.12A = 1884 ----------- Equation (1).

Similarly Now,

Case 2 :-

→ (S + 12% of S) + (A + 10% of A) = 1890

→ S(1 + 12%) + A(1 + 10%) = 1890

→ 1.12S + 1.1A = 1890 ----------- Equation (2).

___________________

Multiply Equation (1) By 1.12 and Equation (2) by 1.1 we get,

→ 1.12[1.1S + 1.12A = 1884] => 1.232S + 1.2544A = 2110.08

→ 1.1[1.12S + 1.1A = 1890] => 1.232S + 1.21A = 2079

Subtracting Them , we get,

→ (1.232S + 1.2544A) - (1.232S + 1.21A) = 2110.08 - 2079

→ 1.232S - 1.232S + 1.2544A - 1.21A = 31.08

→ 0.0444A = 31.08

→ (444A)/10000 = (3108/100)

→ 444A = 310800

→ A = Rs.700

__________________

Now, we have :-

→ CP of Airbag = 700

→ Gain% = 12% (in case 1)

→ SP = [CP * (100+P%)] / 100

→ SP = (700 * 112)/100

→ SP = Rs.784.

And, All over SP in case 1 is 1884.

So,

→ SP of Suitcase = 1884 - 784

→ SP of suitcase = 1100

→ Gain% = 10% ( in case 1.)

→ CP = (SP * 100) / (100 + gain%)

→ CP = (1100 * 100) / 110

→ CP = Rs.1000 .

Hence, Cost Price of Suitcase is Rs.1000 & cost Price of Airbag is Rs.700.