Question

Tow computer were purchased for $16000 each. One was sold at gain of 5% and other at loss of 4% . Find the overall gain or loss % in the whole transaction.​

Answer 1

Question :-

Two computer were purchased for $ 16000 each. One was sold at gain of 5% and other at loss of 4%. Find the overall gain or loss % in the whole transaction.

$\large\underline{\sf{Solution-}}$

Given that,

Two computer were purchased for $ 16000 each. One was sold at gain of 5% and other at loss of 4%.

Case :- 1

Cost Price of computer = $ 16000

Gain % = 5 %

We know,

$\boxed{\sf{  \:\rm \: Selling\:Price \: = \: \frac{(100 + Gain\%) \times Cost \: Price}{100} \: \: }}$

So, on substituting the values, we get

$\rm \:SP_1 =  \:\dfrac{(100 + 5) \times 16000}{100}$

$\rm \: SP_1 = 105 \times 160$

$\rm\implies \:SP_1 \: = \: 16800$

Case :- 2

Cost price of computer = $ 16000

Loss % = 4 %

We know,

$\boxed{\sf{  \:\rm \: Selling\:Price \: = \: \frac{(100 - Loss\%) \times Cost \: Price}{100} \: \: }}$

So, on substituting the values, we get

$\rm \: SP_2 = \dfrac{(100 - 4) \times 16000}{100}$

$\rm \: SP_2 = 96 \times 160$

$\rm\implies \:SP_2 = 15360$

Now, we have

Total Cost price of two computers = $ 32000

Total Selling Price of two computers = 16800 + 15360 = $ 32160

It means, Selling Price > Cost Price

It means, there is gain in this transaction

So,

$\rm \: Gain\% = \dfrac{Selling\:Price - Cost \: Price}{Cost \: Price} \times 100\%$

$\rm \: Gain\% = \dfrac{32160 - 32000}{32000} \times 100\%$

$\rm \: Gain\% = \dfrac{160}{32000} \times 100\%$

$\rm \: Gain\% = \dfrac{1}{2} \%$

$\rm\implies \:\rm \: Gain\% = 0.5 \%$

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{Gain = \sf S.P. \: – \: C.P.} \\ \\ \bigstar \:\bf{Loss = \sf C.P. \: – \: S.P.} \\ \\ \bigstar \: \bf{Gain \: \% = \sf \Bigg( \dfrac{Gain}{C.P.} \times 100 \Bigg)\%} \\ \\ \bigstar \: \bf{Loss \: \% = \sf \Bigg( \dfrac{Loss}{C.P.} \times 100 \Bigg )\%} \\ \\ \\ \bigstar \: \bf{S.P. = \sf\dfrac{(100+Gain\%) or(100-Loss\%)}{100} \times C.P.} \\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$

Answer 2

$\: \sf \fbox \red{Question}$

Two computer were purchased for $16000 each. One was sold at gain of 5% and other at loss of 4% . Find the overall gain or loss % in the whole transaction.

$\: \sf \fbox \red{Answer}$

= two computer where purchased for $16000 each

= then the total cost prices is :-

$\sf \: = 16000 + 16000 \\ \sf = 32000$

= so the total cost prices is $32000

= the first computer was sold at 5% gain than the gain is :-

$\sf \: = Gain = \frac{gain \: percentage}{100} \times cost \: price \\ \\ \sf \: = \: \frac{5}{100} \times 16000 \\ \sf \: = 5 \times 160 \\ \sf \: = 800 \\ \\ \sf Gain\: of \: first \: computer\: = 800$

= so the selling price of first computer is :-

$\sf \: = Gain + cost \: price \\ \sf \: = 800 + 16000 \\ \sf = 16800$

= show the cost price of first computer is $ 16800

= now the loss is 4% on the second computer then the loss is :-

$\sf \: = loss \: = \frac{loss \: percentage}{100} \times \: cost \: price \\ \\ \sf \: = \: \frac{4}{100} \times 16000 \\ \sf \: = 4 \times 160 \\ \sf \: = 640 \\ \\ \sf \: the \: loss \: of \: first \: computer \: is \: = 640 \:$

= so the selling price of the second computer is

$\sf \: = cost price - loss \\ \sf = 16000 - 640 \\ \sf = 15360$

= so the total selling price is

$\sf \: = 16800 + 15360 \\ \sf \: = 32160$

= so here the selling price is greater than cost price so there is profit

= the profit is

$\sf \: = Profit \: = 32160 - 32000 \\ \sf \: = 160$

= now the gain percentage is

$\sf \: = \frac{Gain}{cost \: price } \times 100 \\ \sf \: = \frac{160}{32000} \times 100 \\ \sf \: = \frac{160}{320} \\ \sf \: = 0.5$

$\sf \fbox \red{Gain = 0.5}$

Ans :- 0.5%