Question

[Maths]
Topic: Profit n Loss

A music system when sold for rupees ₹4500 gives a loss of 16.66% to a merchant who sells it. Calculate his loss or gain percent if he sells it for rupees ₹5703.75.
Options:-
(i) Loss of 5.625%
(ii) Profit of 8.33%
(iii) Loss of 7%
(iv) Profit of 5.625%
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Request To Answerers:
>> Please solve it in easiest and best method.
>> No plagiarism​

Answer 1

Answer:

Answer is well rounded off to profit of 5.625 percent

Explanation:

S. P of music system = ₹4500

Incurred loss on S. P = 16.66%

Let C. P be x

So x- (16.66/100)x = ₹4500

83.34x/100 = 4500

x = 4500× 100/83.34

x= ₹5399.5

New S.P of music system = 5703.75

Gain percent = (Gain/ C. P )× 100

= (304.25/5399.5) × 100

= 0.05634×100

= 5.6347%

Sorry took a lot of time ¶¶

Answer 2

$\mathrm{Let\ the\ cost\ price\ be\ 'x'.}\\ \\ \mathrm{Given\ that\ selling\ for \ 4500\ gives\ a\ loss\ of\ 16.66\%\ .} \\ \\ \boxed{\mathrm{Note:\ 16.66\% = \dfrac{1}{6} \times 100\ \%}}} \\ \\ \\ \implies \mathrm{x \ \times \ \Big(1- \dfrac{1}{6}\Big) = 4500}\\ \\ \implies \mathrm{\dfrac{5x}{6}=4500} \\ \\ \implies \mathrm{x = 5400}$

$\mathrm{We\ now\ know\ the\ cost\ price\ of\ the\ musics\ system.} \\ \\ \mathrm{and\ we\ can\ note\ that\ 5400 < 5703.75. }\\ \\ \mathrm{Which\ means\ we\ have \ a\profit\ hence\ option\ i \ and\ iii \ are\ eliminated.} \\ \\ \mathrm{Lets \ find \ the\ profit\ percentage\ now\ .} \\ \\ \mathrm{Profit= 5703.75 - 5400 = 303.75} \\ \\ \implies \mathrm{Profit\ \% = \dfrac{303.75}{5400}\ \times 100 = 5.625\ \%} \\ \\ \boxed{\mathrm{Therefore\ by\ selling\ it\ for\ 5703.75\ we\ have\ a\ profit\ of \ 5.625\%}}$

Hope this helps : )