Question

two positive integers are in ratio 4 : 5 is to 7 is added to each integer their ratio becomes 5:6 then the smallest integer is​

Answer 1

Given:

• 2 positive integers are in the ratio 4:5
• 7 is added to each integer.
• The new ratio becomes 5:6

To find:

→ Smallest integer = ?

Method:

Let the integer be x.

According to the question,

$\dfrac{4x + 7}{5x + 7} = \dfrac{5}{6}$

$\implies 6(4x + 7) = 5(5x + 7)$

$\implies 24x + 42 = 25x + 7$

$\implies42 - 7 = 25x - 24x$

$\implies \boxed{ \bf{x = 35}}$

The 2 integers are in the ratio 4:5

Out of the 2 the smaller integer is 4x

4x = 4(35) = 140

Therefore, the smaller integer is 140

Know more:

Whenever the 2 numbers are in a particular ratio, we always convert them into fraction and analyse the question.

The ratio which is smaller is the smaller integer.