Question

Two numbers are in the ratio of 5:6. If 7 is subtracted from each of them, the ratio becomes 4:5.Find the numbers?

Answer 1

Ratio of Numbers=5:6

Let 1st Number=5x

Let 2nd Number=6x

If 7 is Subtract from both=4:5

A/q

$\frac{5x - 7}{6x - 7} = \frac{4}{5} \\ \\ 5(5x - 7) = 4(6x - 7) \\ \\ 25x - 35 = 24x - 28 \\ \\ 25x - 24x = - 28 + 35 \\ \\ x = 7$

1st Number=5x=5×7=35

2nd Number=6x=6×7=42

$\boxed{\mathtt{\huge{1st\:Number=35}}}$

$\boxed{\mathtt{\huge{2nd\:Number=42}}}$

Ratio=a:b=a/b

Answer 2

$\mathfrak{Answer:}$

1st no. = 35.

2nd no. = 42.

$\mathfrak{Step-by-Step\;Explanation:}$

$\underline{\bold{Given\;in\;the\;Question:}}$

• Ratio of two numbers = 5 : 6.
• If 7 is subtracted from each number then new ratio becomes 4: 5.

$\mathbb{SOLUTION:}$

Let the first and second no. be 5x and 6x .

After subtracting 7 , new number :

• First no. = 5x - 7.
• Second no. = 6x - 7.

$\mathfrak{According\;to\;question:}\\\\\\\implies\tt{\dfrac{5x-7}{6x-7}=\dfrac{4}{5}}\\\\\\\implies\tt{(5x-7)5=(6x-7)4}\\\\\\\implies\tt{25x-35=24x-28}\\\\\\\implies\tt{25x-24x=35-28}\\\\\\\implies\tt{x=7.}\\\\\\\\\boxed{\boxed{\bold{1st\;number=35.\quad\&\quad 2nd\;number=42.}}}$