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Subject :IMO    Class : Class 7

A number consists of two digits whose sum is 9. If 27 is added to the number, its digits are interchanged. Which of the given steps is CORRECT to find the number?
Step 1 :Let the unit’s digit be x
Step 2 :Then, ten’s digit = (9 – x)
∴ Number = 10 × (9 – x) + x
⇒ 90 – 10x + x = (90 – 9x)
Step 3 :Adding 27 to the number 90 – 9x, we get 117 – 9x
Step 4 :Number with digits interchanged is 10x + (9 – x) = 9x + 9
Step 5 :117 – 9x = 9x + 9
Step 6 :Therefore unit’s digit = 6 and ten’s digit = 3
Step 7 :Hence the number = 36.

A Only Step 4
B Both Step 1 and Step 2
C Step 1, 2, 3 and 4
D All steps are correct


how to find the solution

Ans 1:

Class : Class 6
The space means addition

Ans 2:

Class : Class 7
Correct answer is D.

Ans 3:

Class : Class 6
*x 3=y

Ans 4:

Class : Class 7

Ans 5:

Class : Class 8
Nitin , I think you forgot that the sum of the digits of a number should be 9 , As in teh question. All teh other nummbers given by you except 36 is wrong because their digits do nto sum up to 9

Ans 6:

Class : Class 6
The number is not only 36 (It is a number , but there are other numbers) . If you keep x as the ten's digit of the original number and y as the unit's digit of the number , any number following : x 3=y , will follow this rule .The numbers following this rule is 14 27=41 , 25 27=52 , 36 27=63 , 47 27=74 , 58 27=85 , 69 27=96 .

Ans 7:

Class : Class 6

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