Question

selling price of 20 watches is equal to the cost price of 16 watches find the gain percent​

Answer 1

Appropriate Question :-

If selling price of 20 watches is equal to the cost price of 16 watches. Find the loss percent.

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

Given that,

Selling price of 20 watches is equal to the cost price of 16 watches.

Let assume that

Cost price of 1 watch be Rs x

Cost Price of 16 watches be Rs 16 x

Cost Price of 20 watches be Rs 20 x

Now, as it is given that

Selling price of 20 watches is equal to the cost price of 16 watches.

So,

Selling Price of 20 watches = Rs 16x

Now we have

Cost Price of 20 watches = Rs 20 x

Selling Price of 20 watches = Rs 16 x

It means, SP < CP

It implies, there is loss in this transaction.

Now,

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

So, on substituting the values, we get

$\rm \: Loss\% = \frac{20x - 16x}{20x} \times 100 \: \%$

$\rm \: Loss\% = \frac{4x}{20x} \times 100 \: \%$

$\rm \: Loss\% = \frac{1}{5} \times 100 \: \%$

$\rm\implies \:\rm \: Loss\% = 20 \: \%$

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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

Answer:

Given that:-

The Selling price(S.P) of 20 watches is equal to the cost price(C.P) of 16 watches.

To Find:-

Gain percent = ?

Solution:-

20 (S.P) = 16 (C.P)

S.P = (16/20) C.P

S.P = (4/5) C.P ...(1)

And gain is given by

Gain = S.P - C.P

Gain percent

»» (Gain × 100)/C.P

»» [((S.P - C.P)×100)/CP] ..(2)

Put the value of selling price from equation(1) in equation(2)

»» (4/5 C.P-C.P)/C.P × 100

»» 4C.P-5 C.P / 5C.P × 100

»» -1/5 × 100

»» -20%

Therefore,

The Gain percent is -20% and the minus indicates the loss.

Hence, the loss is 20%.