Question

two number are in ratio 5:6 if 5 is added to both the number then the ratio of the ratio of the number become 6:7 find the number​

Answer 1

lif 5 is added to both the figures the new ratio becomes 6:7.07

Answer 2

Question:

• Two numbers are in the ratio 5 : 6. If 5 is added to both the numbers, then the ratio of the numbers becomes 6 : 7. Find the numbers.

Ansnwer:

• The numbers are -25 and -30.

Given:

• Two numbers are in the ratio 5 : 6.
• If 5 is added to the numbers then the ratio of the numbers becomes 6 : 7.

To Find:

• Values of the numbers = ??

Process:

To find the values of the numbers we will let the numbers be 5x and 6x. Then after adding 5 to the numbers we will get (5x + 5) and (6x + 5). As it is given that after adding 5 to the original numbers the ratio of the numbers become 6 : 7 so, we can form an equation as follows:

• $\mathtt{\dfrac{5x+5}{6x+5}=\dfrac{6}{7}}$

After solving the equation we will get the value of x and we will substitute the value of x to 5x and 6x to get the answer.

Solution:

Let the numbers be 5x and 6x.

Adding 5 to the numbers, we get:

5x = (5x + 5)

6x = (6x + 5)

∵ (5x + 5) : (6x + 5) = 6 : 7

$\therefore\sf{\dfrac{5x+5}{6x+5}=\dfrac{6}{7}}$

After cross multiplication, we get:

7(5x + 5) = 6(6x + 5)

After opening the brackets, we get:

35x + 35 = 36x + 30

After transposing like terms on the same side, we get:

36x - 35x = 30 - 35

Solving further, we get:

x = - 5

Hence, the value of x is - 5.

Therefore, first number = 5x = -25

and second number = 6x = -30