Question

The age of a boy can be formed by reversing the digits of his grandfather ‘s age.if the sum of the digits used in his age is 9 and the grandfather is 63 years older then his grandson,find their present age

Answer 1

꧁SOLUTION꧂

✧♥༻༺♥✧

✼GIVEN✼

• The age of boy can be formed by
• reversing the digits of his
• grandfather's age

✼FIND-THEIR PRESENT AGE

✼LET

• THE ONES DIGIT BE X
• THE TENS DIGIT BE Y
• THE PRESENT AGE OF BOY=10y+x
• THE PRESENT AGE OF GRAND PA=10x+y

✼ACCORDING TO THE QUESTION✼

➞10y+X=10x+y-63

➞10x-x+y-10y=63

➞9x-9y=63

➞x-y=7..........(1)

✼SUM OF TWO DIGITS

➞x+y=9........(2)

✼PUTTING TOGETHER EQ 1 AND 2

➞x-y=7

➞x+y=9

➞2x=16

➞x=8

✼PUTTING THE VALUE OF X EQ 2

➞x+y=9

➞8+y=9

➞y=9-8

➞y=1

✼HENCE

➞The present age of grandfather

➞10x+y

➞10*8+1

➞81 years

➞The present age of grandson

➞10y+X

➞10*1+8

➞18years

Answer 2

The present age of the boy is 18 years and the present age of grandfather is 81 years .

Given:

• The age of a boy can be formed by reversing the digits of his grandfather ‘s age.
• If the sum of the digits used in his age is 9 and the grandfather is 63 years older then his grandson.

To find:

• Find their present ages?

Solution:

Formula/Concept to be used:

1. The expanded form of a two digit 'xy' number is (10x+y).
2. Write equations from the given statement and solve.

Step 1:

Write equations from the statements.

Let the age of the boy be 'b' years and the age of grandfather be 'g' years.

It is clear that, The age of the boy is in 2 digits.

Let

$b = xy$

or, we can write it as $\bf b = 10x + y$

and age of grandfather; $\bf g = 10y + x$

ATQ

The age of a boy can be formed by reversing the digits of his grandfather ‘s age and grandfather is 63 years older.

$\bf b= g-63$

So,

$10x + y =10y + x - 63$

$9x - 9y = - 63$

$\bf \: x - y = - 7...eq1$

Again, the sum of digits of boy age is 9, so

$\bf x + y = 9...eq2$

Step 2:

Solve equation 1 and eq2.

Add both equations,

$x - y = - 7\\ x + y = 9 \\ - - - - - - - \\ 2x = 2$

$\bf x = 1$

Put the value of x in eq2;

$\bf y= 8$

Age of boy (xy)= 18 years

Age of grandfather (yx)= 81 years

Thus,

The present age of the boy is 18 years and the present age of grandfather is 81 years .

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