Solving Statements For A Two Digit Number


 
 
Concept Explanation
 

Solving Statements For A Two Digit Number

Sum of the digits of a two digit number is 7. When we interchange the digits, it is found that the resulting two digit new number is greater than the original number by 27. Then the two digit number is

Let the two digit number be x,y

[ i.e., digit at units place be 'y' and digit at tens place be x]

therefore   the two digit number can be expresses as

Rightarrow : : 10x+y

Number obtained by reversing the digits is

Rightarrow : : 10y+x

Now according to question

New number - Original number = 27

(10y+x)-(10x+y)=27

therefore : : : : 9y-9x=27

Rightarrow : : : : y-x=3

Rightarrow : : : : y=3+x                                                                              ................ (1)

Also it is given that

 small dpi{100} x+y=7                                                                                      ................. (2)

From (1) and (2)

Rightarrow : : : : x+(3+x)=7

Rightarrow : : : : 2x+3=7

Rightarrow : : : : 2x=4

Rightarrow : : : : x=frac {4}{2}=2

From (1)  y=3+2=5

therefore    the original number  (xy)=25.

Sample Questions
(More Questions for each concept available in Login)
Question : 1

Two numbers are in the ratio 5 : 3. If they differ by 18, then. The numbers are ________________

Right Option : A
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Explanation
Question : 2

Two numbers are such that the ratio between them is 3 : 5. If each is increased by 10, the ratio between the new numbers so formed is 5:7. Find the original numbers.

Right Option : C
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Explanation
Question : 3

Sum of the digits of a two digit number is 9. When we interchange the digits, it is found that the resulting two digit new number is greater than the original number by 27. Then the two digit number is

Right Option : B
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Explanation
 
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