Question

solve it mathematics​

Answer 1

★ Solution :-

The given ratio (fraction) is 3/2.

We are given with an extra info that 3 is subtracted from first term (numerator) and 4 is subtracted from second term (denominator). So, the fraction is,

$\sf \leadsto \dfrac{3x - 3}{2x - 4}$

The obtained fraction when we subtract the following numbers from first and second term is,

$\sf \leadsto \dfrac{5}{3}$

Now, we are asked to find the number. So, according to the question,

$\sf \leadsto \dfrac{3x - 3}{2x - 4} = \dfrac{5}{3}$

$\sf \leadsto 3(3x - 3) = 5(2x - 4)$

$\sf \leadsto 9x - 9 = 10x - 20$

$\sf \leadsto 9x - 10x = -20 + 9$

$\sf \leadsto -1x = -11$

$\sf \leadsto x = 11$

Now, let's find out the number (fraction).

Original rational number :-

$\sf \leadsto \dfrac{3x}{2x}$

$\sf \leadsto \dfrac{3(11)}{2(11)}$

$\sf \leadsto \dfrac{33}{22}$

Therefore, the number is 33/22.

Answer 2

★ Question ↓

The ratio of two numbers is $\frac{3}{2}$. If 3 is subtracted from the first and 4 from the second, the ratio becomes $\frac{5}{3}$. Find the number.

★ Solution ↓

» Let the numbers be 3x and 2x, then :-

→ $\frac{3x}{2x}$

» Now, subtracting 3 from the numerator and 4 from the denominator :-

→ $\frac{3x - 3}{2x - 4}$

» On subtracting we will get :-

→ $\frac{5}{3}$

» Now, According to question :-

→ $\frac{3x - 3}{2x - 4} = \frac{5}{3}$

→ 3(3x - 3) = 5(2x - 4)

→ 3(3x) - 3(3) = 5(2x) - 5(4)

→ 9x - 9 = 10x - 20

→ 9x - 10x = -20 + 9

→ -x = -11

» Value of -x = -11

Then, Value of x = 11

Original Number :-

=⟩ $\frac{3x}{2x}$

=⟩ $\frac{3(11)}{2(11)}$

=⟩ $\frac{33}{22}$(Answer)

Therefore, we have found the number and that number is $\frac{33}{22}$.