Question

6. The ratio of two numbers is 2 : 7. If 14 is added to each of the numbers, then the ratio of the new numbers becomes 4: 7. What are the original numbers? (দুটা সংখ্যাৰ অনুপাত 2: 7। যদি প্ৰতিটো সংখ্যাৰ লগত 14 যােগ কৰা হয়, তেন্তে নতুন সংখ্যা দুটাৰ অনুপাত 4: 7। সংখ্যা দুটা কি কি?)​

Answer 1

Given

• Ratio of two numbers = 2:7.
• 14 is added to both numbers.
• New ratio = 4:7.

To Find

• Original numbers.

Solution

Let,

• The first number = 2x.
• The second number = 7x.

When 14 is added,

• The first number = 2x + 14.
• The second number = 7x + 14.

According to the question,

(2x + 14)/(7x + 14) = 4/7

Cross - multiplying

=> 7(2x + 14) = 4(7x + 14)

=> 14x + 98 = 28x + 56

=> 98 - 56 = 28x - 14x

=> 42 = 14x

=> x = 42/14

=> x = 3

Substituting value of x = 3 in the assumed numbers,

• First number = 2x = 2×3 = 6.
• Second number = 7x = 7×3 = 21.

Hence, original numbers are 6 and 21.

_________________________________________