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Tag: COORDINATEGEOMETRY

  • Let’s explore another problem that is commonly asked in the CBSE Class 9 exam pattern…

    Question

    The sum of the digits of a two-digit number is 9. If 27 is subtracted from the number, its digits are reversed. Find the number.

    Solution

    Step 1: Define the variables

    Let the two-digit number be 10x+y10x + y, where:

    • xx is the digit in the tens place.
    • yy is the digit in the units place.

    Step 2: Write the given conditions as equations

    1. The sum of the digits is 9: x+y=9.(1)x + y = 9 \tag{1}.
    2. If 27 is subtracted from the number, the digits are reversed: 10x+y−27=10y+x⇒9x−9y=27⇒x−y=3.(2)10x + y – 27 = 10y + x \quad \Rightarrow \quad 9x – 9y = 27 \quad \Rightarrow \quad x – y = 3 \tag{2}.

    Step 3: Solve the equations

    From equation (2): x−y=3⇒x=y+3.(3)x – y = 3 \quad \Rightarrow \quad x = y + 3 \tag{3}.

    Substitute x=y+3x = y + 3 into equation (1): (y+3)+y=9.(y + 3) + y = 9. 2y+3=9⇒2y=6⇒y=3.2y + 3 = 9 \quad \Rightarrow \quad 2y = 6 \quad \Rightarrow \quad y = 3.

    Substitute y=3y = 3 into equation (3): x=y+3=3+3=6.x = y + 3 = 3 + 3 = 6.

    Step 4: Write the solution

    The number is: 10x+y=10(6)+3=63.10x + y = 10(6) + 3 = 63.

    Verification

    1. The sum of the digits is: 6+3=96 + 3 = 9 (correct).
    2. Subtracting 27 from 63 gives 63−27=3663 – 27 = 36, which is the reverse of 63 (correct).

    This problem ensures the following are covered:

    1. Algebraic representation of word problems.
    2. Logical derivation and substitution.
    3. Verification of the result.

    Would you like me to graphically represent another scenario or explain additional examples? PLZ

    COOMENT…..