Question

2 numbers are in the ratio 5:6 if 20 is added to each of them the ratio becomes 7:8 the number are​

Answer 1

Given :

• Ratio of two numbers = 5 : 6
• When 20 is added to 5 : 6 , the ratio becomes 7 : 8

To find :

• The numbers.

Solution :

Ratio of the two numbers = 5 : 6

Let the first number be 5x

and the second number be 6x.

Now, according to the question,

$\sf\:20~when~added~to~5:6~it~becomes~7:8$

• First number + 20 = 5x + 20
• Second number + 20 = 6x + 20

Henceforth , converting word problem in the form of equation,

$\sf\to\:5x+20:6x+20=7:8$

Same can be written as

$\sf\to\:\frac{5x+20}{6x+20}=\frac{7}{8}$

Solving it

$\sf\to\:8( 5x+20)=7(6x+20)$

$\sf\to\:40x+160=42x+140$

$\sf\to\:40x-42x=140-160$

$\sf\to\:\cancel{-}2x=\cancel{-}20$

$\sf\to\:x=\cancel{\frac{20}{2}}$

$\bf\to\:x=10$

Henceforth,

• First Number = 5x = 5 × 10 = 50
• Second Number = 6x = 6 × 10 = 60

Verification :

$\sf\:\frac{5x+20}{6x+20}=\frac{7}{8}$

$\sf\leadsto\:\frac{5(10)+20}{6(10)+20}=\frac{7}{8}$

$\sf\leadsto\:\frac{50+20}{60+20}=\frac{7}{8}$

$\sf\leadsto\:\frac{7\cancel{0}}{8\cancel{0}}=\frac{7}{8}$

$\sf\leadsto\:\frac{7}{8}=\frac{7}{8}$

Hence Verified!~