The ratio of the divisor to the remainder is 3 : 2 and the ratio of the divisor to quotient is 7: 12. If the remainder is 14, then the remainder when the dividend is divided by 9 is:

The ratio of the divisor to the remainder is 3 : 2

divisor : remainder = 3 : 2    Eq.(i)

The ratio of the divisor to quotient is 7: 12.

divisor : quotient = 7: 12    Eq.(ii)

Merage Eq.(i) and Eq.(ii), by multiplying 7 and 3 respectively.

divisor : remainder : quotient = $$3\times7 : 2\times7 : 3\times12$$

= 21 : 14 : 36

If the remainder is 14, then from the above-given ratios divisor and quotient will be 21 and 36 respectively.    Eq.(iii)

As we know that

Dividend = Divisor $$\times$$ Quotient + Remainder

So we can put the Eq.(iii) in the above equation to obtain the value of 'Dividend'.

Dividend = 21 $$\times$$ 36 + 14

= 756+14

= 770

Now dividend(770) is divided by 9 = $$85\frac{5}{9}$$

So 5 will be the remainder.