SOLVING WORD PROBLEMS BASED ON TWO DIGIT NUMBER

Solving Word Problems Based on Two Digit Number :

We consider two digit number as xy. Here y is the number at the unit place and x is the number at the ten's place.

By writing xy in the expanded form, we get

xy  =  10x + 1y

Example 1 :

A two digit number is four times the sum of its digits and twice the product of the digits. Find the number.

Solution :

Let xy be the required two digit number.

xy = 4(x + y)

10x + y  =  4x + 4y

10x - 4x + y - 4y  =  0

6x - 3y  =  0

2x - y  =  0

y  =  2x-----------(1)

xy  =  2 ⋅ x ⋅ y

10x + 1y  =  2xy -----------(2)

Applying (1) in (2), we get

10x + 1(2x)  =  2x(2x)

10x + 2x  =  4x2

12x  =  4x2

x  =  12/4

x  =  3

By applying the value of x in (1), we get

y  =  2(3)

y  =  6

Hence the required two digit number is 36.

Example 2 :

A two digit number such that the product of its digits is 21. When 36 is subtracted from the number the digits are interchanged. Find the number.

Solution :

Let xy be the required two digit number.

A two digit number such that the product of its digits is 21

⋅ y  =  21

y  =  21/x  ---- (1)

When 36 is subtracted from the number the digits are interchanged

xy - 36  =  yx

10x + y - 36  =  10y + x

10x - x + y - 10 y  =  36

9x - 9y  =  36

Dividing it by 9, we get

x - y  =  4  --- (2)

By applying (1) in (2), we get

x - (21/x)  =  4

x2 - 21  =  4x

x- 4x - 21  =  0

x2 - 7x + 3x - 21  =  0

x(x - 7) + 3(x - 7)  =  0

(x - 7) (x + 3)  =  0

 x - 7  =  0x  =  7 x + 3  =  0x  =  -3

By applying the value of x in (1), we get

y  =  21/x

y  =  21/7

y  =  3

Therefore the required two digit number is 73.

Example 3 :

A two digit number is such that the product of its digits is 12. When 36 is added to this number the digits are interchanged. Find the numbers.

Solution :

Let xy be the required two digit number

A two digit number such that the product of its digits is 12

x ⋅ y  =  12

y  =  12/x  ---- (1)

When 36 is added to the number the digits are interchanged

xy + 36  =  yx

10x + y + 36  =  10y + x

10x - x + y - 10y  =  -36

9x - 9y  =  -36

Dividing it by 9, we get

x - y  =  -4  ---- (2)

By applying (1) in (2)

x - (12/x)  =  -4

x2 - 12  =  -4 x

x+ 4x - 12  =  0

(x - 2) (x + 6)  =  0

 x - 2  =  0x  =  2 x + 6  =  0x  =  -6

By applying the value of x in (1), we get

y  =  12/x

y  =  12/2

y  =  6

Therefore the required two digit number is 26.

After having gone through the stuff given above, we hope that the students would have understood how to solve word problems involving two numbers.

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