Question

If there is a gain of 25/4% in selling an article, then the ratio of the gain and
the sale price is one of the following
(a) 17:1 (b) 1:17 (c) 17:25 (d) 25:17​

Answer 1

Answer:

1 : 17

Step-by-step explanation:

Given,  profit % = 25/4 %

$=> \frac{SP-CP}{CP}\times 100 \% = \frac{25}{4} \%\\\\\\=> \bigg(\frac{SP}{CP} - \frac{CP}{CP} \bigg) = \frac{25}{4} \times \frac{1}{100}\\\\ => \frac{SP}{CP} - 1 = \frac{1}{16}\\\\\ => \frac{SP}{CP} = \frac{17}{16}$

     We need to find gain/SP  or  (SP - CP)/SP ,  we need SP in the denominator,  

$=> \frac{CP}{SP} = \frac{16}{17}$

     Now, we need SP - CP in the numerator,  we can get that on subtracting these from 1

$=> 1 - \frac{CP}{SP} = 1 - \frac{16}{17}\\\\ => \frac{SP-CP}{SP} = \frac{17-16}{17}\\\\ =>\frac{Gain}{SP} = \frac{1}{17}$

      Required ratio is 1 : 17

Answer 2

Answer :

25/4 % = Profit (in %) ( Given in Question )

Hence,

$\sf ↝ \frac{ SP - CP}{CP} × 100 = \frac{25}{4} \%$

We can write it like this

$\sf ↝\frac{SP}{CP} - \frac{CP}{CP} × 100 = \frac{25}{4} \%$

$\sf ↝\frac{SP}{CP} - 1 = \frac{\frac{25}{4}}{100}$

$\sf ↝\frac{SP}{CP} - 1 = \frac{\cancel{25}}{4 × \cancel{100}_{\: \: \cancel{25} × 4}}$

$\sf ↝\frac{SP}{CP} -1 = \frac{1}{4 × 4}$

$\sf ↝ \frac{SP}{CP} = \frac{1}{16} + 1$

$\sf ↝ \frac{SP}{CP} = \frac{1}{16} + \frac{16}{16}$

$\sf ↝ \frac{SP}{CP} = \frac{17}{16}$

$\sf \longrightarrow$ we Can Write it like this

$\sf ↝ \frac{CP}{SP} = \frac{16}{17}$

For gain, we need SP - CP ( = gain )

So, we need to subtract 1 from both sides

$\sf ↝ 1 - \frac{CP}{SP} = 1 - \frac{16}{17}$

Take LCM of SP (LHS) , Take LCM of 17 (RHS)

$\sf ↝ \frac{ SP - CP }{SP} = \frac{17 - 16}{17}$

$\sf ↝ \frac{ SP - CP }{SP} = \frac{1}{17}$

Now , we have SP - CP = gain hence,

We can write like this

$\sf ↝\frac{Gain}{SP} = \frac{1}{17}$

Now ratio of gain and sale price = 1 : 17

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For more information :

• Profit, P = SP – CP; SP>CP
• Loss, L = CP – SP; CP>SP
• P% = (P/CP) x 100
• L% = (L/CP) x 100
• SP = {(100 + P%)/100} x CP
• SP = {(100 – L%)/100} x CP
• CP = {100/(100 + P%)} x SP
• CP = {100/(100 – L%)} x SP
• Discount = MP – SP
• SP = MP -Discount
• For false weight, profit percentage will be P% = (True weight – false weight/ false weight) x 100.
• When there are two successful profits say m% and n%, then the net percentage profit equals to (m+n+mn)/100
• When the profit is m% and loss is n%, then the net % profit or loss will be: (m-n-mn)/100
• If a product is sold at m% profit and then again sold at n% profit then the actual cost price of the product will be: CP = [100 x 100 x P/(100+m)(100+n)]. In case of loss, CP = [100 x 100 x P/(100-m)(100-n)]
• If P% and L% are equal then, P = L and %loss = P2/100

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I hope it helps you ❤️✔️