Question

two numbers are in the ratio 5:6 . if 7 is subtracted from each of the numbers ,the ratio becomes 4;5.find the numbers

Answer 1

Given two numbers in ratio = 5 : 6,

Let the common ratio be x ,so the number becomes,

5x and 6x

According to question if seven is substracted,5x -7 and 6x-7 there ratio will become 4: 5

$\frac{5x - 7}{6x - 7} = \frac{4}{5}$

On cross multiplying ,

5 (5x - 7) = 4 (6x -7)

25 x - 35 = 24 x - 28

25 x - 24 x =-28 +35

x = 7

So,the numbers are,

5x = 5 ×7 =35

6x = 6× 7 = 42

Answer 2

$\textbf{\underline{\underline{Answer :-}}}$

$\textsf{One number is 35 and another is 42}$

$\textbf{\underline{\underline{Explanation :-}}}$

$\textsf{\underline{\underline{Given :}}}$

Ratio = 5:6

When 7 is substracted it becomes = 4:5

$\textsf{\underline{\underline{To find :}}}$

The actual numbers

$\textsf{\underline{\underline{Solution : }}}$

Consider the ratio 5:6 as 5x : 6x

Corresponding fractions of 5:6 and 4:5

$\tt{\Rightarrow \dfrac{5x}{6x } \: \: and \: \: \dfrac{4}{5} }$

Equation =

$\tt{\implies \dfrac{5x - 7}{6x - 7} = \dfrac{4}{5} }$

Cross Multiplication =

$\tt{\implies5(5x - 7) = 4(6x - 7)}$

$\tt{\implies25x - 35 = 24x - 28}$

$\tt{\implies25x - 24x = - 28 + 35}$

$\tt{\implies \: x = 7}$

${\large{\boxed{\sf{x = 7}}}}$

$\bf{Value\:of\:5x =}$

$\tt{\implies5 \times 7}$

$\tt{\implies35}$

$\large{\boxed{\sf{First \: number = 35}}}$

$\textbf{Value of 6x =}$

$\tt{\implies6 \times 7}$

$\tt{\implies42}$

$\large{\boxed{\sf{Second \: number = 42}}}$

$\therefore$$\textsf{\underline{One number is 35 and another is 42}}$

$\textbf{\large{\underline{Verification :-}}}$

$\tt{\implies \dfrac{(5 \times 7) - 7}{(6 \times 7)- 7} = \dfrac{4}{5} }$

$\tt{\implies \dfrac{35 - 7}{42 - 7} = \dfrac{4}{5} }$

$\tt{\implies \dfrac{28}{35} = \dfrac{4}{5} }$

Reduce it by 7

${\boxed{\boxed{\tt{\implies \dfrac{4}{5} = \dfrac{4}{5} }}}}$

$\large{\boxed{\sf{LHS = RHS }}}$

$\therefore$$\textsf{\underline{One number is 35 and another is 42}}$