Question

The ratio of two numbers is 5:6. If each number is increased by 8, the ratio becomes 6:7 Find the numbers?​

Answer 1

Step-by-step explanation:

Given :-

The ratio of two numbers is 5:6.

If each number is increased by 8 then the ratio becomes 6:7 .

To find :-

The two numbers

Solution :-

Given that

The ratio of two numbers = 5:6

Let they be 5X and 6X

If each number is increased by 8 then the two numbers will be (5X+8) and (6X+8)

The new ratio = (5X+8) : (6X+8)

According to the given problem

The new ratio = 6:7

Therefore, (5X+8) : (6X+8) = 6:7

=> (5X+8) / (6X+8) = 6 / 7

On applying cross multiplication then

=> 6(6X+8) = 7(5X+8)

=> 36X + 48 = 35X+56

=> 36X-35X = 56-48

=> X = 8

Therefore, X = 8

If X = 8 then 5X = 5(8) = 40

If X = 8 then 6X = 6(8) = 48

Therefore, the numbers are 40 and 48

Answer :-

The two numbers are 40 and 48 respectively.

Check :-

The two numbers are 40 and 48

Their ratio = 40:48

= 40/48

= (5×8)/(6×8)

= 5/6

= 5:6

If 8 is added to both numbers then they will be 40+8 = 48 and 48+8 = 56

The new ratio = 48:56

= 48/56

= (6×8)/(7×8)

= 6/7

= 6:7

Verified the given relations in the given problem.

Used formulae:-

→ a:b can be written as a/b

Answer 2

Step-by-step explanation:

Given :

• The ratio of two numbers is 5:6.
• If each number is increased by 8, the ratio becomes 6:7.

To Find :

• The numbers?

Solution :

Let us assume that the numbers be 5x and 6x.

~When each number is increased by 8, the new numbers are :

• 5x + 8
• 6x + 8

This means, new ratio is :

• 5x + 8 : 6x + 8

This is equal to 6:7.

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

Now, let's solve it!

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

Cross, multiplying,

$\sf : \implies7(5x + 8) = 6(6x + 8) \\ \\ \sf : \implies(7 \times 5x) + 7(8) = (6 \times 6x) + 6(8) \\ \\ \sf : \implies35x + 56 = 36x + 48 \\ \\ \sf : \implies56 - 48 = 36x - 35x \\ \\ : \implies \boxed{ \bf 8 = x} \: \bigstar$

Now, the numbers are :

• 5x = 5(8) = 40
• 6x = 6(8) = 48

Thus, the numbers are 40 & 48.