Question

two numbers are in the ratio 7 is to 6 if 2 is subtracted from the first number and 6 from the second number then the ratio becomes 4 is to 3 determine the two numbers​

Answer 1

Given :

• Two numbers are in the ratio 7:6.
• If 2 is subtracted from the 1st number and 6 from 2nd number, ratio becomes 4:3

To Find :

• The two numbers

Solution :

Let x be the common multiple of the ratio.

•°• First Number = 7x

Second Number = 6x

Case 1 :

2 is subtracted from the first number (7x) and 6 from the second number (6x)

•°• First Number = (7x-2)

Second Number = (6x-6)

Ratio = 4:3

Equation :

$\sf{\dfrac{(7x-2)}{(6x-6)}\:=\:\dfrac{4}{3}}$

$\sf{3(7x-2) =\:4(6x-6) }$

$\sf{21x-6=24x-24}$

$\sf{21x-24x=-24+6}$

$\sf{-3x=-18}$

$\sf{x=\dfrac{18}{3}}$

$\sf{x=6}$

Substitute x = 6 in the ratio value,

$\large{\boxed{\sf{\green{First\:Number\:=\:7x\:=\:7(6)=42}}}}$

$\large{\boxed{\sf{\green{Second\:Number\:=\:6x\:=\:6(6)=36}}}}$

Answer 2

$\large\green{\underline{\underline{\bf{\orange{Given}}}}}$

Two numbers are in the ratio 7 is to 6 if 2 is subtracted from the first number and 6 from the second number then the ratio becomes 4 is to 3

$\large\green{\underline{\underline{\bf{\orange{Find\:out}}}}}$

Determine the two numbers

$\large\green{\underline{\underline{\bf{\orange{Solution}}}}}$

Let the first number be 7x then other number be 6x

According to the given condition

$\implies\sf \Large\frac{7x-2}{6x-6}=\Large\frac{4}{3}$

$\implies\sf 3(7x-2)=4(6x-6)$

$\implies\sf 21x-6=24x-24$

$\implies\sf 24-6=24x-21x$

$\implies\sf 18=3x$

$\implies\sf x=\Large\cancel\frac{18}{3}=6$

$\therefore\sf x=6$

$\large{\boxed{\bf{First\:number=7x=7×6=42}}}$

$\large{\boxed{\bf{Second\:number=6x=6×6=36}}}$

$\large\green{\underline{\underline{\bf{\orange{Verification}}}}}$

$\implies\sf \Large\frac{7x-2}{6x-6}=\Large\frac{4}{3}$

LHS

$\implies\sf \Large\frac{7x-2}{6x-6}$

Substitute the value of x = 6

$\implies\sf \Large\frac{7×6-2}{6×6-6}$

$\implies\sf \Large\frac{42-2}{36-6}$

$\implies\sf \Large\frac{40}{30}$

$\implies\sf \Large\frac{4}{3}$=RHS verified