**Explanation :**a:b=5:9 and b:c=4:7= (4*9/4): (7*9/4) = 9:63/4 a:b:c = 5:9:63/4 = 20:36:63.

**Explanation :**Let the fourth proportional to 4, 9, 12 be x.

Then, 4 : 9 : : 12 : x --- > 4 x x=9x12

X=(9 x 12)/14=27; Fourth proportional to 4, 9, 12 is 27.

**Explanation :**\(\frac {X}{Y}\)=\(\frac {3}{4}\)

=\(\frac {(4x+5y)}{(5x+2y)}\)

= \(\frac{4( x/y)+5)}{(5 (x/y)-2)}\)

=\(\frac{(4(3/4)+5)}{(5(3/4)-2)}\)

=\(\frac{(3+5)}{(7/4)}\)=\(\frac {32}{7}\)

**Explanation :**Sum of ratio terms = (5 + 3) = 8. First part = Rs. (672 * (5/8)) = Rs. 420; Second part = Rs. (672 * (3/8)) = Rs. 252.

**Explanation :**. Sum of ratio terms = (35 + 28 + 20) = 83. A's share = Rs. (1162 * (35/83))= Rs. 490; B's share = Rs. (1162 * (28/83))= Rs. 392; C's share = Rs. (1162 * (20/83))= Rs. 280.

**Explanation :**Let the number of 50 p, 25 P and 10 p coins be 5x, 9x and 4x respectively.

(5x/2)+( 9x/ 4)+(4x/10)=206

50x + 45x + 8x = 4120

1O3x = 4120

x=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.

**Explanation :**Let the quantity of alcohol and water be 4x litres and 3x litres respectively 4x/(3x+5)=4/5 20x=4(3x+5)8x=20 x=2.5 Quantity of alcohol = (4 x 2.5) litres = 10 litres.

**Explanation :**Let the third proportional to 16 and 36 be x.

Then, 16 : 36 : : 36 : x ---> 16 x x = 36 x 36 ---> x=(36 x 36)/16 =81

Third proportional to 16 and 36 is 81.

**Explanation :**Mean proportional between 0.08 and 0.18 \(\sqrt {0.08}\) * 0.18 =\(\sqrt {8}\)/100 * 18/100= \(\sqrt {144}\)/(100 * 100)= 12/100 =0.12