331

Marked price = Rs.180
Selling price = Rs. 108 and
The second discount = 25%
Let x be the first discount
\(\mathrm{S} . \mathrm{P}=\left(1-\frac{x}{100}\right)\left(1-\frac{25}{100}\right) \times M . P\)
\( 108 =\left(1-\frac{x}{100}\right)\left(1-\frac{25}{100}\right) \times 180 \\ 108 =\left(1-\frac{x}{100}\right)\left(\frac{3}{4}\right) \times 180 \)
\(108 =\left(1-\frac{x}{100}\right) \times 135 \\ 1-\frac{x}{100} =\frac{108}{135} \)
\(1-\frac{x}{100} =\frac{4}{5} \\ \therefore \frac{x}{100} =1-\frac{4}{5} \)
\(\frac{x}{100} =\frac{1}{5} \)
\(x=\frac{100}{5}=20\)
The first discount = 20%

Rs.104

Let x and y be the cost price of the two sarees
Saree I                             
Gain = 10%                     
x + 10% of x = 2200       
\( x+\frac{10}{100} x =2200 \)
\(\frac{110}{100} x =2200 \)
\(\frac{11}{10} x =2200 \)
\(x =\frac{2200 \times 10}{11} \)
\(x =Rs. 2000\)
Saree II
Loss = 12%
y-12% of y = 2299
\( y-\frac{12}{100} y =2200 \)
\(\frac{88 y}{100} =2200 \)
\(\frac{22 y}{25} =2200 \)
\(y =\frac{2200 \times 25}{22} \)
\(y =Rs.2500 \)
Total cost price of both sarees = 2000 + 2500
= 4500
But total selling price = 2x 2200
= 4400
Loss : C.P-S.P
= 4500 - 4400 = Rs.100
\(\text { Loss % }=\frac{100}{4500} \times 100\)
\(=\frac{20}{9}=2 \frac{2}{9} \%\)
The loss percentage of the saIes = \(2 \frac{2}{9} \%\)

(i) The cost of the Medicines
= Rs. 800 + GST 5%
\(=800+800 \times \frac{5}{100}\)
= 800 + 40
= Rs.840
(ii) The cost of the cosmetics
= Rs. 650 + GST 12%
\(=650+650 \times \frac{12}{100}\)
= 650+78
= Rs. 728
(iii) The cost of cereals
= Rs. 900 + GST 0%
= 900 + 0 = Rs. 900
(iv) The cost of the sunglass
= Rs. 1750 + GST 18%
\(=1750+1750 \times \frac{18}{100}\)
= 1750 + 315
= Rs. 2065
(v) The cost of Air conditioner
= Rs. 28500 + GST 28%
\(=28500+28500 \times \frac{28}{100}\)
= 28500 +7980
= Rs. 36480
The total bill amount
= 840 +728 + 900 + 2065 + 36480
= Rs. 41013

700cm

Marked price of the AC = Rs. 38000
Option-I                        Option-II
S. P = Rs.38000             Discount = 8%
Gifts = Rs. 3000             S.P = 38000 - 8% of 38000
\(=38000-\frac{8}{100} \times 38000\)
= 38000 - 3040 = Rs. 34960
Discount of 8% is better.

Let x be the C.P of the speaker
x - 768 = 20% of x
\( x-768 =\frac{20}{100} x \)
\(x-768 =\frac{x}{5} \)
\(x-\frac{x}{5} =768 \)
\(\frac{5 x-x}{5} =768 \)
\(\frac{4 x}{5} =768 \)
\(x=\frac{768 \times 5}{4}=960\)
C.P of the speaker is Rs. 960. 
In order to get gain 20%
Then the rate of the speaker = 960 + 20 % of 960
\(=960+\frac{20}{100} \times 960\)
= 960 + 192 = 1152
To get 20% gain,he should sell the speaker for Rs. 1152.

Let x be the cost price of the article.
810 - x = x - 530
2x = 810 + 530
2x = 1340
x = 670
The cost price of the article is Rs. 670.

Let x be the cost price of the article.
x-10% of x = 820
\(x-\frac{10}{100} x=820\)
\( \frac{90 x}{100} =820 \)
\(\frac{9}{10} x =820 \)
\(x =\frac{8200}{9}=911.11\)
Rs.911.11