Question

The ratio of cp and mp is 8:15 and the ratio of profit percent and discount percent is 25:24

Answer 1

Given :

The ratio of cost price to market price = 8 : 15

The ratio of profit percentage to discount percentage = 25 : 24

To Find :

The difference between profit percentage and discount percentage

Solution :

∵ discount % = $\dfrac{market price - selling price}{market price}$

i.e   d % = 1 - $\dfrac{s.p}{m.p}$            .............1

And

Profit % = $\dfrac{selling price - cost price}{cost price}$

i.e  p% = $\dfrac{s.p}{c.p}$ - 1                ...................2

As,   $\dfrac{d}{p}$  = $\dfrac{25}{24}$

Or,  $\dfrac{1-\dfrac{s.p}{m.p} }{\dfrac{s.p}{c.p}-1 }$  = $\dfrac{25}{24}$

∵  ratio of cost price to market price = 8 : 15

Let the cost price  = 8 x

Let the market price = 15 x

So,   $\dfrac{1-\dfrac{s.p}{15x} }{\dfrac{s.p}{8x}-1 }$  = $\dfrac{25}{24}$

Or,    $\dfrac{\dfrac{15x-s.p}{15x} }{\dfrac{s.p-8x}{8x} }$  = $\dfrac{25}{24}$

Or,   $\dfrac{15x-s.p}{15x}$ × $\dfrac{8x}{s.p-8x}$ = $\dfrac{25}{24}$

Or,   $\dfrac{120x-8s.p}{15s.p-120x}$ = $\dfrac{25}{24}$

By cross multiplication

24 × ( 120 x - 8 s.p ) = 25 × ( 15 s.p - 120 x)

Or,  2880 - 192 s.p = 375 s.p - 3000 x

Or,   3000 x + 2880 x = 375 s.p + 192 s.p

Or,  5880 x = 567 s.p

∴          s. p = $\dfrac{567}{5880 x}$

i.e selling price = $\dfrac{567}{5880 x}$

Now, from eq 1

d % = 1 - $\dfrac{\dfrac{567}{5880x} }{15x}$

From eq 2

 p% = $\dfrac{\dfrac{567}{5880x} }{8x}$  - 1

Now, Difference between p% and d% =  ( $\dfrac{\dfrac{567}{5880x} }{8x}$  - 1  ) - (  1 - $\dfrac{\dfrac{567}{5880x} }{15x}$ )

                                                               = $\dfrac{\dfrac{567}{5880x} }{8x}$  + $\dfrac{\dfrac{567}{5880x} }{15x}$

                                                               = $\dfrac{567}{735}$ + $\dfrac{567}{392}$

                                                               = 0.771 + 1.446

                                                               = 2.217

Hence, The Difference between profit percentage and discount percentage is 2.217 %   Answer

Answer 2

Step-by-step explanation:

Given The ratio of cp and mp is 8:15 and the ratio of profit percent and discount percent is 25:24 . Find the difference between Profit% and Discount%

• Let the cost price = 8 m
• So marked price = 15 m
• Let profit percentage = 25 p%
• So Discount percentage = 24 p %
• Now equating both profit and discount we get
• 8m(100 + 25 p) / 100 = 15 m (100 – 24 p) / 100
• 8 (100 + 25 p) = 15(100 – 24 p)
• 800 + 200 p = 1500 – 360 p
• 200 p + 360 p = 1500 – 800
• 560 P = 700
• Or p = 700 / 560
• Or p = 5/4
• Now Discount % = 24 x 5/4 = 30%
• So profit % = 25 x 5/4 = 125 / 4 = 31.2%
• So difference between Profit% and Discount% will be = 31.2 – 30
•                                                                      = 1.2%

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