Let C1 be the cost price of the first article and C2 be the cost price of the second article.
Let the first article be sold at a profit of 22%, while the second one be sold at a loss of 8%.
We know, C1 + C2 = 600.
The first article was sold at a profit of 22%. Therefore, the selling price of the first article = C1 + (22/100)C1 = 1.22C1
The second article was sold at a loss of 8%. Therefore, the selling price of the second article = C2 - (8/100)C2 = 0.92C2.
The total selling price of the first and second article = 1.22C1 + 0.92C2.
As the merchant did not make any profit or loss in the entire transaction, his combined selling price of article 1 and 2 is the same as the cost price of article 1 and 2.
Therefore, 1.22C1 + 0.92C2 = C1+C2 = 600
As C1 + C2 = 600, C2 = 600 - C1. Substituting this in 1.22C1 + 0.92C2 = 600, we get
1.22C1 + 0.92(600 - C1) = 600
or 1.22C1 - 0.92C1 = 600 - 0.92*600
or 0.3C1 = 0.08*600 = 48
or C1 = 48/(0.3) = 160.
If C1 = 160, then C2 = 600 - 160 = 440.
The item that is sold at loss is article 2. The selling price of article 2 = 0.92*C2 = 0.92*440 = 404.80.
? ( 22 x r2) / 7 = 38.5
? r2 =(38.5 x 7) /22
? r = 3.5 cm
? Circumference = 2 x (22/7) x 3.5 cm
= 22 cm
S.P = P.W of Rs. 2200 due 1yr hence = Rs. [(2200 x 100)/100+(10 x 1)] = Rs.2000
Gain = Rs.(2000-1950) = Rs. 50
PW = = Rs.2500
TD = Amount - PW = 2800 - 2500 = Rs.300
P.W. = Rs. (1600 - 160) = Rs. 1440
? S.I. on Rs.1440 at 5% is Rs. 160.
? Time = [100 * 160 / 1440 * 5] = 20/9 years = [20/9 * 12] months = 27 months.
? s= (13 + 5 + 12) / 2 cm
= 15cm
s-a = 2 cm,
s-b = 10 cm and
s-c = 3 cm
? Area = ? (15 x 2 x 10 x 3 ) cm2
= 30 cm2
? (12 x h) / 2 = 30
? h = 5 cm
Let lateral side = (5y) cm and base = (4y) cm
? perimeter = 5y + 5y + 4y = 14
?y = 1
So, the sides are 5 cm , 5 cm and 4 cm
Now s= 1/2 (5 + 5 + 4) cm = 7 cm
(s-a) = 2 cm
(s-b) = 2 cm and
(s-c) = 3 cm
? Required Area = ? (7 x 2 x 2 x 3) cm2
=2?21 cm2
s = (13 + 14 + 15 ) / 2 = 21,
s-a = 8 ,
s-b = 7,
s-c= 6
? Area to be painted = ? [s(s-a) (s-b) (s-c)]
=? [21 x 8 x 7 x 6] m2
= 84 m2
? Cost of painting = Rs. (84 x 8.75) = Rs. 735
Area = ?r2 = 0.49?
? r = 0.7 m
Number of revolutions = total distance / circumference
= (1.76 x 1000) / (2 x 22/7 x 0.7)
= 400
Distance travelled in 1 revolution = circumference of the wheel
= ?d
= ( 22/7 ) x 63
= 198 cm
So the distance travelled in 100 revolutions = 100 x distance travelled in 1 revolution
= 100 x 198 cm
= 19800 cm
= 198 m
Circumference of a circular = 2?r
? 2 x (22 / 7) x r = 440
? r = [440 x (7/22) x (1/2)] = 70 m
? Radius of outer circle = (70 + 14) m
= 84 m
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