RATIO PROPORTIONS AND VARIATIONS CONTINUED - PUNJAB-CURRICULUM-AND-TEXTBOOK-BOARD-PCTB / 10TH-CLASS / MATHEMATICS / MATHEMATICS-10-10TH-CLASS-NBF-2024 / VARIATIONS / RATIO-PROPORTIONS-AND-VARIATIONS-CONTINUED

If 2 is added in each number of the ratio 3 : 4, we get a new ratio 5 : 6. Find the numbers.

Solution: Because the ratio of two numbers is 3: 4.

Multiply each number of the ratio with $x$ . Then the numbers be $3x$ , $4x$ and the ratio becomes $3x:4x$ . Now according to the given condition

\frac{3 x + 2}{4 x + 2} = \frac{5}{6}

6 (3 x + 2) = 5 (4 x + 2) \Rightarrow 18 x + 12 = 20 x + 10

18 x - 20 x = 10 - 12 \Rightarrow - 2 x = - 2 \Rightarrow x = 1

Thus the required numbers are

3x = 3(1) = 3

and $4x = 4(1) = 4$

3.1 Ratio, Proportions and Variations (Continued)