Question

The ratio between the present ages of Ravi and Jai is 3: 2 If Ravi was 6 years older to Jai four years back, how old in Jai now?
 (A) 6 years
(B) 12 years
(C) 18 years
(D) Data Inadequate

Answer 1

Hint: We will consider the common factor of present ages then also by condition we will calculate the common factor.

Complete step-by-step answer:
Given that the ratio between the present ages of Ravi and Jai is 3: 2. Suppose$x$be the common factor between them.
Therefore, present age of Ravi $ = 3x$ and present age of Jai $ = 9x$
Now, according to Question
4 years back Ravi is 6 years older than from Jai
Therefore mathematically,
Four your back Ravi age $ = 3x - 4$
Four year $\operatorname{back} $ Jai age $ = 2x - 4$
By condition, $3x - 4 = 2x - 4 + 6$
$ \Rightarrow \;\;\;{\kern 1pt} 3x = 2x + 6 \Rightarrow 3x - 2x = 6$
$ \Rightarrow \;\;\;{\kern 1pt} x = 6$
Therefore, the common factor between ages is 6.
Now, the present age of Ravi = $3 \times 6 = 18$ years.
Present age of Jai $ = 2 \times 6 = 12$ years.
Hence, (c) is the correct option.

Additional Information: In mathematics, a ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8∶6, which is equivalent to the ratio 4∶3). Similarly, the ratio of lemons to oranges is 6∶8 (or 3∶4) and the ratio of oranges to the total amount of fruit is 8∶14 (or 4∶7).

Note: The relation between two numbers which shows how much bigger one quantity is than another. The numbers in a ratio may be quantities of any kind, such as counts of people or objects, or such as measurements of lengths, weights, time, etc. In most contexts, both numbers are restricted to be positive