Question

The sum of the digits of a two digit number is 7. If the digits are reversed, the new number decreased by 2, equals twice the original number. Find the number.​

Answer 1

GIVEN:

• The sum of the digits of a two digit number is 7
• If the digits are reversed, the new number decreased by 2, equals twice the original number.

TO FIND:

• What is the original 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)

✧ The sum of the digits of a two digit number is 7

According to question:-

➾ x + y = 7

➾ x = 7 –y....❶

CASE:- 2)

✧ If the digits are reversed, the new number decreased by 2, equals twice the original number.

◇ Reversed Number = 10y + x

◇ New Number –2 = 2(Original Number)

According to question:-

➾ 10y + x –2 = 2(10x + y)

➾ 10y + x –2 = 20x + 2y

➾ –2 = 20x + 2y –10y –x

➾ –2 = 19x –8y

Put the value of 'x' from equation 1)

➾ –2 = 19(7–y) –8y

➾ –2 = 133 –19y –8y

➾ –2 –133 = –27y

➾ –135 = –27y

➾ $\sf{\cancel\dfrac{-135}{-27}}$ = y

❮ 5 = y ❯

Put the value of 'y' in equation 1)

➾ x = 7 –5

❮ x = 2 ❯

• NUMBER = 10x + y
• NUMBER = 10(2) + 5
• NUMBER = 20 + 5
• NUMBER = 25

❝ Hence, the number formed is 25 ❞

______________________

Answer 2

$\sf{\underline{\boxed{\large{\blue{\mathsf{Correct\: Question}}}}}}$

• The sum of the digits of a two digit number is 7. If the digits are reversed, the new number decreased by 2, equals twice the original number. Find the number.

_______________________

$\sf{\underline{\boxed{\large{\blue{\mathsf{Solution}}}}}}$

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• Sum of 2 digits of 2 digit no. = 7
• If the digits are reversed the new number decreased by 2 equals twice the original numbers .

_______________________

$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

• The original number = ???

______________________

$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

let the original no. be 10x + y

• Sum of 2 digits of 2 digit no. is 7

$\sf\implies x + y = 7$------( i )

• If the digits are reversed the new number decreased by 2 equals twice the original numbers .

$\sf\implies 10y + x - 2 = 2 ( 10x + y )$

$\sf\implies 10y + x - 2 = 20x + 2y$

$\sf\implies 10y - 2y + x -20x = 2$

$\sf\implies 8y - 19x = 2$--------( ii )

• Multiply eq i by 8

$\sf\implies 8x + 8y = 56$-------- ( iii )

• subtracting eq iii from ii

$\sf\dag 8y - 19x - 8x - 8y = 2 - 56$

$\sf\dag - 27x = -54$

$\sf\dag x = 2$

$\sf{\red{\boxed{\bold{\leadsto x = 2}}}}$

putting value of y in eq . i

$\sf\dag x + y = 7$

$\sf\dag 2 + y = 7$

$\sf\dag y = 7 - 2$

$\sf\dag y = 5$

$\sf{\red{\boxed{\bold{\leadsto y = 5}}}}$

__________________________

$\longrightarrow 10x + y$

$\longrightarrow 10\times 2 + 5$

$\longrightarrow 20 + 2$

$\longrightarrow 25$

$\sf{\pink{\boxed{\bold{\leadsto Original\: no\: = \: 25 }}}}$

______________________

$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• Original number is 25