ʹͲ ʹͶ͵Ͷand by 2nd condition, x 10 2 (y 10 ).......( 2 )
From ( 1 ), we get, x 8 8 y 64
or x 8 y 64 8
or x 8 y 56 .............( 3 )
From ( 2 ), we get, x 10 2 y 20
or 8 y 56 10 2 y 20 [putting the value of x from (3)]
or 8 y 2 y 20 56 10
or 6 y 66
or y 11
? from( 3 ), we get, x 8 u 11 56 88 56 32
? at present, Father’s age is 32 years and son’s age is 11 years.
Example 13. Twice the breadth of a rectangular garden is 10 metres more than its
length and perimeter of the garden is 100 metre.
a. Assuming the length of the garden to be x metre and its breadth to be y metre,
form system of simultaneous equations.
b. Find the length and breadth of the garden.
c. There is a path of width 2 metres around the outside boundary of the garden. To
make the path by bricks, it costs 110 00 per square metre. What will be the
total cost?
Solution : a. Length of the rectangular garden is x metre and its breadth is y metre.
? by 1st condition, 2 y x 10 ........( 1 )
and by 2nd condition, 2 (xy) 100 .......( 2 )
b. From equation (1), we get, 2 y x 10 ........( 1 )
From equation (2), we get, 2 x 2 y 100 .......( 2 )
or 2 xx 10 100 [putting the value of 2 y from (1)]
or 3 x 90
or x 30
? from (1), we get, 2 y 30 10 [putting the value
ofx]
or, 2 y 40
or, y 20
? length of the garden is 30 metres and its breadth
is 20 metres.
c. Length of the garden with the path is (30+4) metres.
= 34 metres