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ANSWER
Let the fathers age be x years and his son be y years.
Therefore, seven years ago, age of father = (x-7)
and age of son = (y - 7)
According to the given condition,
x-7 =7(y-7)
or x-7y = -42 ...(1)
After 3 years, fathers age = x+3 and
son's age = (y+3)
As per given condition,
x+3 = 3(y+3)
x-3y = 6 ...(2)
ON subtracting (2) from (1), we get
x - 7y - (x -3y) = -42 - 6
⇒ -4y = -48
⇒ y = 12
On putting value of y in (2), we get
x - 3(12) = 6
⇒ x = 6 + 36 = 42
Hence, present father's age = 42 years
and present son's age = 12 years.
Let the price of one Bat be x and the price of one ball be y,
Now, According to the question,
From(1) we have
By putting different values of x, we get different corresponding values of y.So
X 100 300 -100
Y 600 500 700
Now, From (2), we have,
By putting different values of x, we get different corresponding values of y.So
X 100 400 -200
Y 400 300 500
Let cost each kg of apples = Rs x
Cost of each kg of grapes = Rs y
Given that The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs 160
So that
2 x + y = 160 … (1)
2x = 160 - y
x = (160 – y)/2
Let y = 0 , 80 and 160 we get
X = (160 – ( 0 ))/2 = 80
X = (160- 80 )/2 = 40
X = (160 – 2* 80 )/2 = 0
X
80
40
0
y
0
80
160
Given that the cost of 4 kg of apples and 2 kg of grapes is Rs 300
so we get
4 x + 2 y = 300 … (2)
Divide by 2 we get
2 x + y = 150
Subtract 2x both side we get
Y = 150 – 2 x
Plug x = 0 , 50 , 100 we get
Y = 150 – 2*0 = 150
Y = 150 – 2* 50 = 50
Y = 150 – 2 * (100 ) = - 50
X
0
50
100
Y
150
50
-50
Algebraic representation
2 x + y = 160 … (1)
4 x + 2 y = 300 … (2)
The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs 160.
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