Question

41. A two-digit number is 4 times the sum of its digits and twice the product of the digits​

Answer 1

GIVEN:

• A two-digit number is 4 times the sum of its digits
• A two digit number is twice the product of the digits

TO FIND:

• What is the number ?

SOLUTION:

Let the digit at unit's place be 'y' and the digit at ten's place be 'x'

• NUMBER = 10x + y

CASE:- 1)

✧ A two-digit number is 4 times the sum of its digits

According to question:-

➨ 10x + y = 4(x + y)

➨ 10x + y = 4x + 4y

➨ 10x –4x = 4y –y

➨ 6x = 3y

Take 3 common from both sides

➨ 2x = y...1)

CASE:- 2)

✧ A two digit number is twice the product of the digits

According to question:-

➨ 10x + y = 2xy...2)

Put the value of 'y' in equation 2)

➨ 10x + 2x = 2x(2x)

➨ $\sf{\cancel{12x} = \cancel{4x^2}}$

➨ 3 = x

Put the value of 'x' in equation 1)

➨ 2 $\times$ 3 = y

➨ 6 = y

• NUMBER = 10x + y
• NUMBER = 10(3) + 6
• NUMBER = 30 + 6
• NUMBER = 36

❝ Hence, the number formed is 36 ❞

______________________

Answer 2

Answer:

⭐ Question ⭐

✏ A two-digit number is 4 times the sum of its digits and twice the product of the digits.

⭐GIVEN⭐

✏A two-digit number is 4 times the sum of its digits.

✏A two digit number is twice the product of the digits.

⭐TO FIND⭐

✏What is the number ?

⭐SOLUTION⭐

✏Let the digit at unit's place be 'y' and the digit at ten's place be 'x'

✏NUMBER = 10x + y

➡CASE:- 1)

✏A two-digit number is 4 times the sum of its digits

✳According to question:-

=> 10x + y = 4(x + y)

=> 10x + y = 4x + 4y

=> 10x –4x = 4y –y

=> 6x = 3y

✍Take 3 common from both sides

✏ 2x = y...1)

➡CASE:- 2)

✏ A two digit number is twice the product of the digits

✳According to question:-

=> 10x + y = 2xy...2)

✍Put the value of 'y' in equation 2)

=> 10x + 2x = 2x(2x)

=> 12x = 4x²

=> 3 = x

✍Put the value of 'x' in equation 1)

=> 2 × 3 = y

=> 6 = y

⭕NUMBER = 10x + y

= 10(3) + 6

= 30 + 6

= 36

⭐ Hence, the number is 36 ✔

Step-by-step explanation:

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