Question

Two numbers are in the ratio 3 : 4, if 6 be added to each terms of the ratio, then the new

ratio will be 4 : 5, then the numbers are​

Answer 1

GIVEN :-

• Two numbers are in the ratio 3 : 4 .
• 6 is added to each terms of the ratio.
• New ratio = 4 : 5.

TO FIND :-

• The numbers.

SOLUTION :-

Let the ratio constant be "x".

★ Numbers are 3x and 4x.

after 6 is added to each term of the ratio :-

★ Numbers are 3x + 6 and 4x + 6

ACCORDING TO QUESTION,

→ (3x + 6)/(4x + 6) = 4/5

By cross multiplication,

→ 4(4x + 6) = 5(3x + 6)

→ 16x + 24 = 15x + 30

→ 16x - 15x = 30 - 24

→ x = 6

Hence we got the value of x = 6.

Now , Numbers are,

→ 3x = 3 × 6 = 18.

→ 4x = 4 × 6 = 24.

Hence,

• [ The the required numbers for this question are 18 and 24 ]

Answer 2

$\mathcal{\pink{\underbrace{\blue{GIVEN:-}}}}$

• Two numbers are in the ratio 3:4 .

• If 6 be added to each terms of the ratio, then the new ratio will be 4:5 .

$\mathcal{\pink{\underbrace{\blue{TO\: FIND:-}}}}$

• The new number .

$\mathcal{\pink{\underbrace{\blue{SOLUTION:-}}}}$

Let,

• First number = x

• Second number = y

☃️ According to the question,

$\orange\bigstar\:\rm{\gray{\overbrace{\underbrace{\purple{\dfrac{x}{y}\:=\:\dfrac{3}{4}\:}}}}}$

$\rm\green{\implies\:x\:=\:\dfrac{3}{4}\times{y}\:}$ ----(1)

✍️ If we added 6 in numerator, then new numerator is “x + 6” .

✍️ If we added 6 in denominator, then new denominator is “y + 6” .

☃️ Again, according to the question

$\green\bigstar\:\rm{\gray{\overbrace{\underbrace{\purple{\dfrac{x\:+\:6}{y\:+\:6}\:=\:\dfrac{4}{5}\:}}}}}$

$\rm{\implies\:5x\:+\:30\:=\:4y\:+\:24\:}$

☞ Putting the value of “x = 3y/4” in the above equation,

$\rm{\implies\:5\times{\dfrac{3}{4}}\times{y}\:+\:30\:=\:4y\:+\:24\:}$

$\rm{\implies\:\dfrac{15y}{4}\:-\:4y\:=\:24\:-\:30\:}$

$\rm{\implies\:\dfrac{15y\:-\:16y}{4}\:=\:-6\:}$

$\rm{\implies\:-y\:=\:-24\:}$

$\rm\red{\implies\:y\:=\:24\:}$

☞ Putting the value of “ y = 8/3 ”

$\rm{\implies\:x\:=\:\dfrac{3}{4}\times{24}\:}$

$\rm\red{\implies\:x\:=\:18\:}$

$\rm\pink{\therefore}$ The first number is “18” and the second number is “24” .