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A two-digit number is 4 times …

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

Posted by Ananda Prsada Lenka 6 years, 8 months ago

CBSE > Class 10 > Mathematics

2 answers

Yogita Ingle 6 years, 8 months ago

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 (i), we get
10/2y + 1/y = 2
5/y + 1/y = 2
6/y = y
∴ y = 3
Hence x = 6
The two digit number is (10y + x) = 10(3) + 6 = 36

0Thank You

Vimla Devi 6 years, 8 months ago

3Thank You

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