Ratio & Proportion :

1.Find a fourth proportional to the numbers.

2, 5, 6.

Solution: Let X be the forth proportional, then

2:5::6:X or 2/5=6/X

∴ X=5 × 6/2=15

2. Find a third proportional to the numbers

2.5, 1.5.

Solution: Let X be the third proportional, then

2.5:1.5::1.5:X or 2.5/1.5=1.5/X

∴ X=1.5 × 1.5/2.5=0.9

3. Find the mean proportional between 108 and 12.

Solution: Let X be the mean proportional. Then,

108:X::X:12 or, 108/X = X/12 or , X²= 1296 or, X = 36

4. Two numbers are in the ratio of 4:5 and the some of this numbers is 54. Find the two numbers.

Solution: Here, a=4, b=5 and x=54.

∴ The first number = ax/a+b=4×54/4+5=24

and, the second number= bx/a+b=5×54/4+5= 30

5.Three numbers are in the ratio of 3:4:8 and the some of these numbers is 1950. Find the three numbers.

Solution: Here, a=3, b=4, c=8 and x=1950

∴ The first number = ax/a+b+c=3×1950/3+4+8=390

the second number= bx/a+b+c=4×1950/3+4+8= 520

and, the third number= cx/a+b+c=8×1950/3+4+8= 1040