Question

Find two numbers in the ratio of $7:12$ so that the greater exceeds the less by 275.

Answer 1

Hint: Here we will consider the variables to the given ratio and for the given condition such that on simplification the two numbers can be computed. We can take one variable as x and other as x+275.

Complete step-by-step answer:
Let the two numbers be ’a’ and ‘b’ and assume that $b > a$.
Given, that $a:b = 7:12$,
Therefore,
 $
   \Rightarrow b - a = 275 \\
   \Rightarrow b = a + 275 \to (1) \\
$
Let us substitute equation (1) in ratio we get
$
   \Rightarrow \dfrac{a}{{a + 275}} = \dfrac{7}{{12}} \\
   \Rightarrow 12a = 7a + \left( {7 \times 275} \right) \\
   \Rightarrow a = 7 \times 55 = 385 \\
$
So the value of $b = a + 275 = 385 + 275 = 660$.
Therefore the two numbers are 385,660.

Note: Always be careful when taking the variable for two numbers as per the condition which is given in the question. Check whether one number is exceeding or preceding another number. Then only we will get the right equation.