Question

two number are in the ratio 5:6 if 8 is
subtract from each, the new number are
in the ratio 4:5 find the number​

Answer 1

Answer :

Two numbers are 40 and 48.

Given :

• Two numbers are in the ratio 5:6.
• If 8 is subtracted from each, the new numbers are in the ratio 4:5.

To find :

• The two numbers.

Solution :

Consider,

• 1st number = 5x
• 2nd number = 6x

According to the question :-

• If 8 is subtracted from each, the new numbers are in the ratio 4:5.

If 8 is subtracted, then →

• 1st number = (5x-8)
• 2nd number = (6x-8)

$\to\sf{(5x-8):(6x-8)=4:5}$

$\to\sf{\dfrac{5x-8}{6x-8}=\dfrac{4}{5}}$

$\to\sf{25x-40=24x-32}$

$\to\sf{25x-24x=-32+40}$

$\to\sf{x=8}$

★ 1st number = 5 × 8 = 40

★ 2nd number = 6 × 8 = 48

_________________

Verification :-

• 1st number = 40
• 2nd number = 48

Ratio = 5:6

→ 40:48 = 5:6

→ 5:6 = 5:6

If 8 is subtracted from each number , the new numbers are in the ratio 4:5.

★ 1st number = (40-8) = 32

★ 2nd number = (48-8) = 40

Ratio = 4:5

→ 32:40 = 4:5

→ 4:5 = 4:5

Hence Verified !

Answer 2

$\large\mathcal{\underbrace{\red{SOLUTION:-}}}$

GIVEN :-

Two numbers are in the ratio ‘5:6’ .

If ‘8’ is subtract from each, then the new numbers are in ratio ‘4:5’ .

✴️ Let,

• the one number be ‘p’ .

• And the other number is ‘q’ .

✍️ According to the question,

• $\rm\longrightarrow{\dfrac{p}{q}\:=\:\dfrac{5}{6}\:}$ -----(1)

• And $\rm\longrightarrow{\dfrac{p\:-\:8}{q\:-\:8}\:=\:\dfrac{4}{5}\:}$ -----(2)

To Find :-

• The original numbers .

CALCULATION :-

✍️ From Equation (1) we get,

$\rm{\implies\:6p\:=\:5q\:}$

$\rm{\boxed{\implies\:6p\:-\:5q\:=\:0\:}}$ ------(a)

✍️ From Equation (2) we get,

$\rm{\implies\:\dfrac{p\:-\:8}{q\:-\:8}\:=\:\dfrac{4}{5}\:}$

$\rm{\implies\:5(p\:-\:8)\:=\:4(q\:-\:8)\:}$

$\rm{\implies\:5p\:-\:40\:=\:4q\:-\:32\:}$

$\rm{\boxed{\implies\:5p\:-\:4q\:=\:8\:}}$ -------(b)

☞ Now, from Equation (a) we get,

$\checkmark\:\rm{\boxed{\implies\:p\:=\:\dfrac{5q}{6}\:}}$

☞ Now, put the value of ‘p’ from above in the equation (b) we get,

$\rm{\implies\:5\times{\dfrac{5q}{6}}\:-\:4q\:=\:8\:}$

$\rm{\implies\:\dfrac{25q}{6}\:-\:4q\:=\:8\:}$

$\rm{\implies\:\dfrac{25q\:-\:24q}{6}\:=\:8\:}$

$\rm{\implies\:1q\:=\:8\times{6}\:}$

$\bigstar\:\rm{\purple{\boxed{\implies\:q\:=\:48\:}}}$

✍️ Now put the value of ‘q = 48’ from Equation (1) we get,

$\rm{\implies\:\dfrac{p}{48}\:=\:\dfrac{5}{6}\:}$

$\rm{\implies\:p\:=\:\dfrac{5}{6}\:\times{48}\:}$

$\rm{\implies\:p\:=\:5\times{8}\:}$

$\bigstar\:\rm{\blue{\boxed{\implies\:p\:=\:40\:}}}$

☞ Therefore,

✔️ One number is ‘40’ .

✔️ Another number is ‘48’ .