Question

7. Ratio of two numbers is 3:8.
On adding 5 to both numbers,
the ratio becomes 2:5. Which is
the smaller number out of the
two? *
O 64
0 120
O45
O 105​

Answer 1

Answer :

45

Explanation :

Ratio of the two numbers is - 3 : 8

Adding 5 to both numbers, the ratio becomes 2 : 5.

Which one is the smaller number?

Let's consider,

• Greater number = 8x
• Smaller number = 3x

Adding 5 to both,

• Greater number = (8x + 5)
• Smaller number = (3x + 5)

Now, the ratio of the new numbers is 2 : 5

According to the question,

→ (3x + 5) : (8x + 5) = 2 : 5

→ (3x + 5)/(8x + 5) = 2/5

→ 5(3x + 5) = 2(8x + 5)

→ 15x + 25 = 16x + 10

→ 25 - 10 = 16x - 15x

→ 15 = x

∴ The smaller number is = 3x = 3(15) = 45.

Answer 2

Answer:

O 45

Step-by-step explanation:

Given -

Ratio of two numbers = 3:8

Ratio of two numbers if we add 5 both = 2:5

To find -

The smaller number

Solution -

Now,

greater number = 8x, smaller number = 3x

after adding 5,

greater number = 3x+5, smaller number = 8x+5

the real ratio after adding 5 = 2:5

so

3x+5 : 8x+5 = 2:5

$=> \frac{3x + 5}{8x + 5} = \frac{2}{5} \\ (after \: cross \: multiplication) \\ (3x + 5) \times 5 = (8x + 5) \times 2 \\ = > 15x + 25 = 16x + 10 \\ = > 15x + 25 - 10 = 16x \\ = > 25 - 10 = 16x - 15x \\ = > 15 = x \\ = > x = 15$

smaller number = 3x

= 3×15

= 45

hence 45 is the smaller number.

hope it helps.