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12 RATIO PROPORTION EXAMPLES
Ex. 1. If a : b = 5 : 9 and b : c = 4: 7, find a : b : c.
Sol. a:b=5:9 and b:c=4:7= (4X9/4): (7x9/4) = 9:63/4
a:b:c = 5:9:63/4 =20:36:63.
Ex. 2. Find:
(i) the fourth proportional to 4, 9, 12;
(ii) the third proportional to 16 and 36;
iii) the mean proportional between 0.08 and 0.18.
Sol.
i) Let the fourth proportional to 4, 9, 12 be x.
Then, 4 : 9 : : 12 : x ó4 x x=9x12 ó X=(9 x 12)/14=27;
Fourth proportional to 4, 9, 12 is 27.
(ii) Let the third proportional to 16 and 36 be x.
Then, 16 : 36 : : 36 : x ó16 x x = 36 x 36 ó x=(36 x 36)/16 =81
Third proportional to 16 and 36 is 81.
(iii) Mean proportional between 0.08 and 0.18
Ö0.08 x 0.18 =Ö8/100 x 18/100= Ö144/(100 x 100)=12/100=0.12
Ex. 3. If x : y = 3 : 4, find (4x + 5y) : (5x - 2y).
Sol. X/Y=3/4 ó (4x+5y)/(5x+2y)= (4( x/y)+5)/(5 (x/y)-2) =(4(3/4)+5)/(5(3/4)-2)
=(3+5)/(7/4)=32/7
Ex. 4. Divide Rs. 672 in the ratio 5 : 3.
Sol. Sum of ratio terms = (5 + 3) = 8.
First part = Rs. (672 x (5/8)) = Rs. 420; Second part = Rs. (672 x (3/8)) = Rs. 252.
Ex. 5. Divide Rs. 1162 among A, B, C in the ratio 35 : 28 : 20.
Sol. Sum of ratio terms = (35 + 28 + 20) = 83.
A's share = Rs. (1162 x (35/83))= Rs. 490; B's share = Rs. (1162 x(28/83))= Rs. 392;
C's share = Rs. (1162 x (20/83))= Rs. 280.
Ex. 6. A bag contains 50 p, 25 P and 10 p coins in the ratio 5: 9: 4, amounting to
Rs. 206. Find the number of coins of each type.
Sol. Let the number of 50 p, 25 P and 10 p coins be 5x, 9x and 4x respectively.
(5x/2)+( 9x/ 4)+(4x/10)=206ó 50x + 45x + 8x = 4120ó1O3x = 4120 óx=40.
Number of 50 p coins = (5 x 40) = 200; Number of 25 p coins = (9 x 40) = 360;
Number of 10 p coins = (4 x 40) = 160.
Ex. 7. A mixture contains alcohol and water in the ratio 4 : 3. If 5 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture
Sol. Let the quantity of alcohol and water be 4x litres and 3x litres respectively
4x/(3x+5)=4/5 ó20x=4(3x+5)ó8x=20 óx=2.5
Quantity of alcohol = (4 x 2.5) litres = 10 litres.