A two digit number is 4 times the sum and twice the product of its digits find the number

Distribute the referral code to your friends and ask them to register with Tutorix using this referral code.

Once we get 15 subscriptions with your referral code, we will activate your 1 year subscription absolutely free.

Your subscribed friend will also get 1 month subscription absolutely free.

>

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

Solution

Let the digit in the ones place be x and tens place be y Hence the two digit number = 10y + x Given that the two digit number = 4 times sum of its digits ⇒ 10y + x = 4(x + y) ⇒ 10y + x = 4x + 4y ⇒ 3x – 6y = 0 ⇒ 3x = 6y ∴ x = 2y → (1) It is also given that the two digit number = 2 times product of its digits ⇒ 10y + x = 2xy

Divide by xy both the sides, we get

10/x + 1/y =2

put x =2y from 1, we get

6/y = 3

so y = 2 and hence x= 6 Hence x = 6

The two digit number is (10y + x) = 10(3) + 6 = 36

Mathematics

Secondary School Mathematics X

Standard X