Question

In a bus, the no. of women is three times the no. of children. The no. of men is 1.5 times the number of women. If the total no. of persons including the driver and conductor is 70, find the no. of men travelling in the bus.

Answer 1

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

Given that,

In a bus, the number of women is three times the number of children.

So, let assume that

↝ Number of children in a bus = x

So,

↝ Number of women in a bus = 3x

Further, given that

↝ The number of men is 1.5 times the number of women.

So,

↝ Number of men = 1.5 × 3x = 4.5 x

Thus, we have

$\red{\begin{gathered}\begin{gathered}\bf\: Number \: of-\begin{cases} &\sf{children = x} \\ &\sf{women = 3x}\\ &\sf{men = 4.5x}\\ &\sf{driver = 1}\\ &\sf{conductor = 1} \end{cases}\end{gathered}\end{gathered}}$

According to statement, Total number of persons = 70

$\red{\rm :\longmapsto\:x + 3x + 4.5x + 1 + 1 = 70}$

$\red{\rm :\longmapsto\:8.5x + 2 = 70}$

$\red{\rm :\longmapsto\:8.5x = 70 - 2}$

$\red{\rm :\longmapsto\:8.5x = 68}$

$\red{\rm \implies\:x = \dfrac{68}{8.5} = \dfrac{68 \times 10}{85} = 8}$

So, we have now

$\red{\begin{gathered}\begin{gathered}\bf\: Number \: of-\begin{cases} &\sf{children = 8} \\ &\sf{women = 3 \times 8 = 24}\\ &\sf{men = 4.5 \times 8 = 36}\\ &\sf{driver = 1}\\ &\sf{conductor = 1} \end{cases}\end{gathered}\end{gathered}}$

• Hence, Number of men traveling in a bus = 36

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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.