Question

A person met a group of people, and he said to them, Good morning, one hundred people
They said to him, our number is not one hundred
If you Twice our number, half and quarter it plus you so we will become a hundred
What is their number? ✨​

Answer 1

Answer :

37 people

Solution :

Let the total people excluding the speaker is x .

Then , twice the people = 2x

A/Q

(Twice the number / half and quarter ) + speaker = 100

Half and quarter = 0.5 + 0.25

= 0.75

$\tt \dfrac{2x}{ 0.75} + 1 = 100$

$\implies \tt \dfrac{2x}{\dfrac{3}{4}} = 100 -1$

$\implies \tt \dfrac {2x \times 4}{3} = 99$

$\implies$ 8x = 99 × 3

$\implies \tt x = \dfrac{99 \times 3}{8}$

x = 37.125

Hence , the group of people excluding the speaker contains 37 people roughly .

Verification :

When 37 is twice , people become = 74 .

half and quarter times 80 = 74 / 0.75

= 98.67

Now , 98.67 + 1 = 99.67 ≈ 100