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Question 1:
If a manufacturer allows 40% commission on the retail price of his product, he earns a profit of 9%. What would be his profit percent if the commission is reduced by 25 percent?
Solution:
We need to find out the profit % when the given commission is reduced by 25 percent.
Given data:
According to the question consider
Cost price (C.P.) of the product = $ 100
Then, a commission of the product = $ 40
Therefore selling price (S.P.) = $ (cost price (C.P.) – commission)
= $ (100 – 40)
= $ 60
Given that profit = 9%
Therefore Cost price (C.P.) = \(\frac { 100 }{ 100+gain%} \)* S.P
So,
C.P. = $ \(\frac { 100 }{ 100+9 } \)* 60
= $ \(\frac { 6000 }{109 } \)
Now new commission = $ 15
Therefore new selling price (S.P.) = $ 100 – 15
= $ 75
Gain = S.P. – C.P.
= $ (75 – \(\frac { 6000 }{109 } \))
= $ \(\frac { 2175 }{109 } \)
Gain% = (\(\frac { Profit }{C.P. } \)*100)%
=(\(\frac { 2175 }{109 } \)*\(\frac { 109 }{6000 } \)*100)%
= 36.25 %
Hence, gain % is 36.25.
Question 2:
After getting two successive discounts, a pant with the least price of $ 200 is available at $ 125. If the second discount is 14%, find the first discount.
Solution:
Let the first discount be ‘P%’
Then, 86% of (100 – P) % of 200 = 125
\(\frac { 86 }{ 100 } \)*\(\frac { (100 – P) }{ 100 } \)*200 = 125
100-P = \(\frac {(125*100*100) }{ 200*86 } \)
100 – P = 72.67
P = 100 – 72.67
P = 27.32%
Therefore, first discount price of pant is 27.32%.
Question 3:
A women sells an article at a profit of 20%. If he had bought it at 15% less and sold it for $ 11.50 less, he would have gained 25%. Find the cost price of the article.
Solution:
Given data:
Consider cost price (C.P.) of article be ‘X’
First selling price of article ‘X’ = 120% of ‘X’
= \(\frac { 120 }{ 100 } \)*X
= \(\frac { 6 }{ 5 } \)*X
Cost price of article for ‘X’ at 75% = 75% of ‘X’
=\(\frac { 75 }{ 100 } \)*X
=\(\frac { 3 }{ 4 } \)*X
Second selling price of article ‘X’ = 125% of 3/4 * X
= \(\frac { 125 }{ 100 } \)*\(\frac { 3x }{ 4 } \)
= \(\frac { 15x }{ 16 } \)
As given the article is sold at $ 11.50 less
Therefore, selling prices are equalized to a reduced price
\(\frac { 6x }{5 } \) –\(\frac { 15x }{ 16 } \) = 11.50
\(\frac { 21x }{80 } \) = 11.50
X = $ 43.8
Almost equal to $ 44
Hence, the cost price of an article is given as $ 44.
Question 4:
A dealer sold three – fourth of his articles at a gain of 25% and the remaining at cost price. Find the profit earned by him in the whole transaction.
Solution:
A dealer sold his ¾ th quantity with a gain of 25% and the remaining ¼ that its cost price.
Given data:
Consider cost price (C.P.) of whole articles be ‘X’
Cost price (C.P.) of \(\frac { 3}{ 4} \)th quantity = $ \(\frac { 3x}{ 4} \)
Cost price (C.P.) of \(\frac { 1}{ 4} \)th quantity = $ \(\frac { x}{ 4} \)
Total selling price (S.P.) = $ ((125% of \(\frac { 3x}{ 4} \)) + \(\frac { x}{ 4} \))
= $ (\(\frac { 15x}{ 16} \) + \(\frac { x}{ 4} \))
= $ (\(\frac { 19x}{ 16} \))
Profit / Gain = S.P. – C.P.
= $ (\(\frac { 19x}{ 16} \) – x)
= $ \(\frac { 3x}{ 16} \).
Gain % = (\(\frac { gain}{ C.P. } \)*100)%
= (\(\frac {3x}{ 16 } \)*\(\frac {1}{ x } \)*100)%
= 18.75%.
Hence, the gain % of the article is 18.75%.
Question 5:
A man sold two flats for $ 775,000 each. On one he gains 18% while on the other he losses 18%. How much does he gain or lose in the whole transaction?
Solution:
In this problem he gets an equal amount of profit and loss such cases there is always a loss. Therefore the selling price (S.P.) is immaterial.
Loss % = (\(\frac {common loss and gain %}{ 10 } \))2
= (\(\frac {18 }{ 10 } \))2
= (\(\frac {324 }{ 100 } \))
= 3.24%
The total loss incurred by the person is 3.24%.
Question 6:
Pure petrol costs $ 100 per lit. After adulterating it with kerosene costing $ 50 per lit, a shopkeeper sells the mixture at the rate of $ 96 per lit, thereby making a profit of 20%. In what ratio does he mix the two?
Solution:
Here, we have two different cost prices for different mixtures and one selling price (S.P.).
Given data:
Cost price (C.P.) of petrol = $ 100 per lit
Cost price (C.P.) of kerosene = $ 50 per lit
Selling price (S.P.) of mixture = $ 96 per lit
As we have two cost prices,
Mean cost price = $(\(\frac {100 }{ 120 } \))* 96)
= $ 80 per lit.
Since they asked us to find a ratio it is easy to find out by the allegation rule
Cost price (C.P.) of a unit Cost price (C.P.) of a unit quantity of $ X item quantity of $ Y item
Mean cost
$ M
(M – Y) (X – M)
Similarly using this concept here,
Cost price (C.P.) of a unit Cost price (C.P.) of a unit quantity of $ 100 item quantity of $ 50 item
Mean cost
$ 80
(80 – 50) (100 – 80)
Therefore, required ratio = 30 : 20
= 3 : 2.
Question 7:
Find cost price (C.P.), when
1. Selling price (S.P.) = $ 50, Gain = 18%
2. Selling price (S.P.) = $ 51, Loss = 14%
Solution:
Here, we need to find cost price (C.P.) using below formulae
1. Given data
Selling price (S.P.) = $ 50 & Gain = 18%
C.P. = \(\frac { 100 + Gain%) }{ 100 } \)*S.P.
=$ \(\frac { 100 + 18 }{ 100 } \)*50= $ 59.
2. Given data
Selling price (S.P.) = $ 51, Loss = 14%
C.P. = \(\frac { 100 – Loss% }{ 100 } \)*S.P.
= $ \(\frac { 100 – 14 }{ 100 } \)*51
= $ 43.86.
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