Question

a number divided into two parts such that one part is 2 less than three times the other part and the numbers are in ratio 5:3. find the number and it's parts.

Answer 1

Let one part of the number be 'x'.

ONE PART IS 2 LESS THAN 3 TIMES THE OTHER PART.

Other part = 3x-2

Ratio = 5:3 i.e. 5/3

Equation:

3x-2/x = 5/3

9x-6 = 5x (by cross multiplication) 
9x - 5x = 6
4x = 6
x = 3/2

One part = 3/2
Other part = 3x-2 = 3*3/2-2 = 9/2-2 = 5/2

Number = 3/2 +5/2 = 8/2 = 4

Proof:
Equation was:
3x-2/x = 5/3
by putting values
(5/2)/(3/2)
5/2 * 2/3 (reciprocal)
5/3 = 5/3
LHS = RHS
Hence Proved

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