Question

The digits at the ten's place of a 2 digit number is two times the digit at the one's place.if the digits are interchanged and add the 15 in the new number that obtained ,then the new numbet will become 3/4 times of original number.find the number.

Answer 1

Let :

• x be the digit at tens place
• y be the digit at one's place
• Therefore original number = 10x + y

GIVEN :

• The digits at the ten's place of a 2 digit number is two times the digit at the one's place.
• Digits are interchanged and 15 is added to new number ,the new number will become 3/4 times of original number

To find :

Original number

Solution :

Part 1)

x = 2y ....... equation 1

Part 2)

1. Digits are interchanged ➝ 10y + x
2. 15 is added to it ➝ (10y+x) + 15
3. New number is (3/4)th of original ➝ 15 + (10y+x) = (3/4){ 10x + y}

$\sf \implies \: \: 10y + x + 15 = \dfrac{3}{4}(10x+y) \\\\\sf put\: value \: of \: x \: from \: equation \: 1 , \: \\ \sf \: into \: above \: equation \: \\ \\ \sf \implies \: 10y + (2y) + 15 = \dfrac{3}{4} \bigg( \: (10 \times 2y) + y \: \bigg) \\ \\ \sf \implies \: 12y \: + 15 = \dfrac{3}{4} \bigg( \: 20y + y \: \bigg) \\ \\ \sf \implies \: (12y + 15) \times 4 = 3 \times 21y \\ \\ \sf \implies \:48y + 60 = 63y \\ \\ \sf \implies \:63y - 48y = 60 \\ \\ \sf \implies \:15y = 60 \\ \\ \sf \implies \:y = \dfrac{60}{15} \\ \\ \sf \implies \:y \: = \: 4$

Now put y = 4 in equation 1

x = 2(4) = 8

Original number = 10x + y = 10(8) + 4

Original number = 80+4

original number = 84

ANSWER : 84