Advertisements
Advertisements
Question
The sum of digits of a two digit number is 13. If the number is subtracted from the one obtained by interchanging the digits, the result is 45. What is the number?
Solution
Let the digits at units and tens place of the given number be x and y respectively. Thus, the number is `10 y + x.`.
The sum of the digits of the number is 13. Thus, we have ` x + y =13`
After interchanging the digits, the number becomes `10 x + y`.
The difference between the number obtained by interchanging the digits and the original number is 45. Thus, we have
`(10 x + y) - (10 y + x)= 45`
`⇒ 10 x + y -10 y -x = 45`
` ⇒ 9 x - 9y = 45`
`⇒ 9(x - y) = 45`
`⇒ x - y = 45/9`
`⇒ x - y = 5`
So, we have two equations
` x + y = 13`
` x - y = 5`
Here x and y are unknowns. We have to solve the above equations for x and y.
Adding the two equations, we have
`( x + y) + ( x - y )= 13 + 5`
`⇒ x + y + x - y = 18`
` ⇒ 2x = 18`
` ⇒ x = 18/2`
`⇒ x = 9`
Substituting the value of x in the first equation, we have
` 9 + y = 13`
` ⇒ y = 13 - 9`
` ⇒ y = 4`
Hence, the number is ` 10 xx4 + 9 = 49 .`
APPEARS IN
RELATED QUESTIONS
Solve `\frac { 2 }{ x } + \frac { 1 }{ 3y } = \frac { 1}{ 5 }; \frac { 3 }{ x } + \frac { 2 }{ 3y } = 2` and also find ‘a’ for which y = ax – 2
Solve `\frac{2}{x+2y}+\frac{6}{2x-y}=4\text{ ;}\frac{5}{2( x+2y)}+\frac{1}{3( 2x-y)}=1` where, x + 2y ≠ 0 and 2x – y ≠ 0
Solve the following systems of equations
(i)`\frac{15}{u} + \frac{2}{v} = 17`
`\frac{1}{u} + \frac{1}{v} = \frac{36}{5}`
(ii) ` \frac{11}{v} – \frac{7}{u} = 1`
`\frac{9}{v} + \frac{4}{u} = 6`
Solve the following pairs of equations by reducing them to a pair of linear equations
`10/(x+y) + 2/(x-y) = 4`
`15/(x+y) - 5/(x-y) = -2`
Formulate the following problems as a pair of equations, and hence find their solutions:
Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current
In a ΔABC, ∠C = 3 ∠B = 2 (∠A + ∠B). Find the three angles.
Solve the following pair of linear equations.
152x − 378y = − 74
− 378x + 152y = − 604
ABCD is a cyclic quadrilateral finds the angles of the cyclic quadrilateral.
On selling a T.V. at 5% gain and a fridge at 10% gain, a shopkeeper gains Rs 2000. But if he sells the T.V. at 10% gain the fridge at 5% loss. He gains Rs 1500 on the transaction. Find the actual prices of T.V. and fridge.
The sum of a two digit number and the number obtained by reversing the order of its digits is 99. If the digits differ by 3, find the number.
