Question

12. Two mumbers are in the ratio of 5:6. If 7 is subtracted from each of the
numbers, the ratio hocomes 4:5. Find the numbers.​

Answer 1

Step-by-step explanation:

$\frac{5}{6} - 7 = \frac{4}{5} \\ \frac{5 - 42}{6} = \frac{4}{5} \\ \\ \frac{ - 38}{6} = \frac{4}{5} \\ 24 = - 190 \\ 12.. - 95$

Answer 2

Question :-

Two numbers are in the ratio of 5:6. If 7 is subtracted from each of the Numbers, the ratio h

becomes 4:5. Find the numbers.

Answer :-

ratio of two numbers is 5:6

let the original numbers are 5x and 6x

• on subtracting 7 from each of the numbers, numbers will be ;

• 5x - 7
• 6x - 7

but according to the question (If 7 is subtracted from each of the numbers, the ratio h

becomes 4:5)

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

so, x = 7 is a common multiple of numbers

then, numbers are

• 5 × 7 = 35
• 6 × 7 = 42

so, two numbers are 35 and 42