Question

the sum of the digits of a two digits number is 12. if the digits are reversed
the new number becomes4/7 times the original number. find the original number.​

Answer 1

ɢɪᴠᴇɴ :-

The sum of the digits of a two digits number is 12. if the digits are reversed

the new number becomes4/7 times the original number.

ᴛᴏ ғɪɴᴅ :-

• Original number
• Reversed number

sᴏʟᴜᴛɪᴏɴ :-

Let tens place digit be x and ones place digit be y

then,

➲ According to 1st condition :-

• Tens place digit + Ones place digit = 12

• x + y = 12. ---(1)

➲ According to 2nd condition :-

• Original number = (10x + y)
• Reversed number = (10y + x)

• Reversed no = 4/7 × Original number

➭ 10y + x = 4/7 × (10x + y)

➭ 7(10y + x) = 4(10x + y)

➭ 70y + 7x = 40x + 4y

➭ 70y - 4y = 40x - 7x

➭ 66y = 33x

➭ 33x - 66y = 0

➭ 33(x - 2y) = 0

➭ x - 2y = 0/33

➭ x = 2y. --(2)

Put x = 2y in (1) , we get,

➭ x + y = 12

➭ 2y + y = 12

➭ 3y = 12

➭ y = 12/3

➭ y = 4

Put y = 4 in (2) , we get,

➭ x = 2y

➭ x = 2×4

➭ x = 8

Hence,

• Tens place = x = 8
• Ones place = y = 4

Therefore,

• Original number (10x + y) = 84
• Reversed number (10y + x) = 48