Question

the ratio of two numbers is 3:4. if 10 is added to each of them, the ratio of the sums is 5:6. find the numbers.​

Answer 1

Answer:

3x = 3 × 5 = 15

4x = 4 × 5 = 20

the numbers are 15 and 20

Answer 2

Topic :-

Ratio and Proportion

Given :-

The ratio of two numbers is 3 : 4. If 10 is added to each of them then ratio between them becomes 5 : 6.

To Find :-

The given numbers.

Solution :-

Let 'x' be a common multiple between the given numbers.

So, numbers become 3x and 4x.

Now, adding 10 to both of them.

New numbers are ( 3x + 10 ) and ( 4x + 10 ).

Now, it is given that their ratio is 5 : 6.

$\dfrac{3x + 10}{4x + 10} = \dfrac{5}{6}$

Now, cross multiply,

6( 3x + 10 ) = 5( 4x + 10 )

18x + 60 = 20x + 50

20x - 18x = 60 - 50

2x = 10

x = 5

So, numbers are :-

3x = 3(5) = 15

4x = 4(5) = 20

Answer :-

So, the numbers are 15 and 20.

Verification :-

$\dfrac{15}{20} = \dfrac{3}{4}$

$\dfrac{15+10}{20+10} = \dfrac{25}{30}=\dfrac{5}{6}$

Numbers are satisfying given conditions.

Hence, verified.