Question

Two numbers are in the ratio 5:6. When 2 is added to the first number and 3 to he second their ratio becomes 4:5 find the numbers.

Answer 1

Answer:

Step-by-step explanation:

Let the two numbers be 5x and 6x respectively.

5x + 2 = 4x

6x + 3 = 5x

5x + 2 / 6x + 3 = 4x / 5x

5x ( 5x + 2 ) = 4x ( 6x + 3 )

25x^2 +10x = 24x^2 + 12x

25x^2 - 24x^2= 12x - 10x

             x^2           = 2x

(x) X (x)        = 2x

x                  = 2x/x

                    = 2

x = 2

Therefore,

The numbers are 10 and 12

Answer 2

Let the first number be A and the second number be B.

Then Acc. to Ques. ;

A /B  = 5 /6   >> A =  5B/6                                .... >  Eq.1

Also,

A + 2 / B + 3 = 4/5

⇒ 5(A + 2) = 4(B + 3)

⇒ 5A + 10 = 4B + 12

⇒ 5A - 4B = 2                                 ..... ⇒ Eq.2

Putting Eq.1 in Eq.2 ;

⇒ (5 x 5B/6) - 4B = 2

⇒25B/6 - 4B = 2

⇒B/6 = 2

∴ B=12

Putting B=12 in Eq.1;

∴ A=10