Question

Two number are in the ratio 4 : 5. If 10 is
subtracted from each, the new numbers are in the
ratio 16:24. The smaller number is?​

Answer 1

Let the number be x

So the ratio of the two numbers will be : 4x:5x

Given that, if 9 is subtracted from each the ratio becomes 3:4

So, our equation will be

(4x-9)/(5x-9)=3:4=3/4

4(4x-9)=(5x-9)3

16x-36=15x-27

16x-15x=36–27

x=9

So, the numbers are 9*4=36 and 9*5=45

Answer 2

Basic Concept Used :-

Writing Systems of Linear Equation from Word Problem.

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.

$\large\underline{\bf{Solution-}}$

Given that two numbers are in the ratio 4 : 5.

$\begin{gathered}\begin{gathered}\bf\: Let \: the \: numbers \: be-\begin{cases} &\sf{4x} \\ &\sf{5x} \end{cases}\end{gathered}\end{gathered}$

☆ If 10 is subtracted from the numbers, then

$\begin{gathered}\begin{gathered}\bf\: Numbers \: are-\begin{cases} &\sf{4x - 10} \\ &\sf{5x - 10} \end{cases}\end{gathered}\end{gathered}$

☆ According to statement, the numbers are in the ratio 16 : 24

$\rm :\longmapsto\:\dfrac{4x - 10}{5x - 10} = \dfrac{16}{24}$

$\rm :\longmapsto\:\dfrac{4x - 10}{5x - 10} = \dfrac{2}{3}$

$\rm :\longmapsto\:12x - 30 = 10x - 20$

$\rm :\longmapsto\:12x - 10x = 30 - 20$

$\rm :\longmapsto\:2x = 10$

$\bf\implies \:x = 5$

Hence,

$\begin{gathered}\begin{gathered}\bf\: Numbers \: are-\begin{cases} &\sf{4x = 4x5 = 20} \\ &\sf{5x = 5 \times 5 = 25} \end{cases}\end{gathered}\end{gathered}$

Therefore,

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \underbrace{ \boxed{ \bf{ \: Smaller \: number \: is \: 20}}}$