Question

17. Two numbers are in the ratio 3:5. If 10 is subtracted
from each of them then the ratio becomes. 1:5. Find the
greater number.
(a) 24
(b) 20
(c) 25
(d) 16​

Answer 1

Answer:

option (b) 20

Step-by-step explanation:

Given :

• Two numbers are in the ratio 3 : 5
• If 10 is subtracted from each of them, then the ratio becomes 1 : 5

To find :

the greater number

Solution :

Let the two numbers be 3x and 5x

→ the greater number = 5x

The ratio becomes 1 : 5 if 10 is subtracted from each of them.

(3x – 10)/(5x – 10) = 1/5

5(3x – 10) = 1(5x – 10)

15x – 50 = 5x – 10

15x – 5x = 50 – 10

10x = 40

x = 40/10

x = 4

The value of x is 4

Substitute x = 4,

5x = 5(4) = 20

Therefore, the greater number is 20

Verification :

The other number = 3x = 3(4) = 12

Condition : If 10 is subtracted from each of them, then the ratio becomes 1 : 5

(12 – 10) : (20 – 10) = 1 : 5

2 : 10 = 1 : 5

2(1) : 2(5) = 1 : 5

1 : 5 = 1 : 5

LHS = RHS

Hence verified!

Answer 2

Given

• Ratio of two numbers = 3 : 5
• 10 is subtracted from each of them, then
• Ratio becomes 1 : 5

To find

• The greater number among them

Solution

Let the two numbers be 3x and 5x, the greater number among them is 5x.

Then, according to the question :-

• (3x - 10) / (5x - 10) = 1 : 5
• (3x - 10) / (5x - 10) = 1 / 5
• 5(3x - 10) = 1(5x - 10)
• 15x - 50 = 5x - 10
• 15x - 5x = - 10 + 50
• 10x = 40
• x = 40/10
• x = 4

Hence, the value of x is 4, then the greater number that is 5x will be :-

• 5x = 5(4) = 20

And the other number, that is 3x will be :-

• 3x = 3(40) = 12

Verification

• (3x - 10) / (5x - 10) = 1 : 5
• (12 - 10) / (20 - 10) = 1 / 5
• (2) / (10) = 1 / 5
• 2 : 10 = 1 : 5
• 1 : 5 = 1 : 5