Question

16. Two years ago, a man's age was three times the square of his son's age. In three
time, his age will be four times his son's age. Find their present ages.
17. A piece of doth costs 175. If the piece were 4 m longer and each metre costs 5 less, the cost would have remained unchanged. how long is the piece.?​

Answer 1

Answer:

Let the man's current age be x and that of his son be y

From first condition,

(x−2)=3(y−2)

2

. ----------(1)

From the second condition,

(x+3)=4(y+3)

x+3=4y+12

x=4y+9 ------------(2)

put the value of x from equation 2 to 1

4y+9−2=3(y

2

+4−4y)

3y

2

−16y+5=0

3y

2

−15y−y+5=0

3y(y−5)−1(y−5)=0

(3y−1)(y−5)=0

so, y=

3

1

. which is not possible

and y=5

son's age x=5 years

father's age =4(5)+9=29 years. (from equation 1)

Step-by-step explanation:

Let the cost of xm cost rs35

and y be the cost of 1m cloth

therefore

xy=35

y=35/x

according to the question

(x+4)(y-1)=35

(x+4)(35/x-1)=35

(x×35/x)-x+(4×35/x)-4=35

35-x+140/x-4=35

-x^2+140-4x ÷ x=35-35

-x^2+140-4x=0

x^2+4x-140=0

x^2+14x-10x-140=0

x (x+14)-10 (x+14)=0

(x-10)(x+14)=0

x=10

y=35/10=3.5

therefore 10m cloth cost Rs35

and cost of 1m cloth is Rs3.5