Question

The ratio of Nutan’s age to Vidya’s age at present is 5:4. If the sum of their ages at present is 36, what is Vidya’s age at present?
(A). The present age of Nutan and Vidya are 30 and 20 years respectively.
(B). The present age of Nutan and Vidya are 20 and 16 years respectively.
(C). The present age of Nutan and Vidya are 25 and 20 years respectively.
(D).Data insufficient.

Answer 1

Note: In this question it is given that the ratio of Nutan’s age to Vidya’s age at present is 5:4. If the sum of their ages at present is 36, then we have to find Vidya’s age. So to find the solution we have to know that whenever we have given a ratio, we have to write each corresponding value as the multiplication of any variable, i.e, if the ratio of their age is a:b then we have to assume that their age is ax and bx, where x is the variable which we have to find from the given condition.

Complete step-by-step solution:
Here it is given that the ratio of Nutan’s age to Vidya’s age at present is 5:4.
So let us consider that Nutan’s age is 5x years and Vidya’s age is 4x years.
Where x be any variable, so we have to find the value of x.
Also in the question it is given that the summation of their present age is 36 years,
So from the above we can write,
(Nutan’s age + Vidya’s age) = 36
$$\Rightarrow 5x+4x=36$$
$$\Rightarrow 9x=36$$
$$\Rightarrow x=\dfrac{36}{9}$$
$$\Rightarrow x=4$$
So the value of x is 4.
Now we can easily find the age of Nutan and Vidya.
$$\therefore$$ Nutan’s age = 5x =$$5\times 4$$= 20 years
Vidya’s age = 4x = $$4\times 4$$= 16 years.
Therefore, the present age of Nutan and Vidya are 20 and 16 years respectively.
Hence the correct option is option B.

Note: So you might be thinking how can we take their age as 5x and 4x, this is because a ratio is basically a fraction and there must be some value that has been canceled from the numerator and denominator in order to get the fraction, and if we consider this canceled term be x, then by multiplying with the numerator and denominator we will get the individual age i.e, 5x and 4x.