10 years ago a man's age was 2 times that of his son. 10 years hence, the ratio of the
ages of the man and his son will be 14:9. Find their present ages.
Answers
AnswEr :
Let the Present Age of Man be x Yrs. and Present Age of Son be y Yrs.
• 10 Years Ago
⇒ Man's Age = 2 × Son's Age
⇒ ( x - 10 ) = 2 × ( y - 10 )
⇒ ( x - 10 ) = ( 2y - 20 )
⇒ x = 2y - 20 + 10
⇒ x = 2y - 10 —(¡)
• 10 Years from Now
⇒ Man's Age : Son's Age = 14 : 9
⇒ ( x + 10 ) / ( y + 10 ) = 14 / 9
⇒ 9 × ( x + 10 ) = 14 × ( y + 10 )
⇒ 9x + 90 = 14y + 140
⇒ 9( 2y - 10) + 90 = 14y + 140 —( from ¡)
⇒ 18y - 90 + 90 = 14y + 140
⇒ 18y = 14y + 140
⇒ 18y - 14y = 140
⇒ 4y = 140
⇒ y = 140 / 4
⇒ y = 35 [ Son Present Age ]
• Using the Value of y = 35 in (¡)
⇒ x = 2y - 10
⇒ x = ( 2 × 35 ) - 10
⇒ x = 70 - 10
⇒ x = 60 [ Man Present Age ]
჻ Present Age of Man and his Son is 60 Yrs. and 35 Yrs. respectively.
Answer:
Age of son = 35 yrs.
Age of His father = 60 yrs.
Step-by-step explanation:
assume the age of father be x and age of son be y.
Their ages before 10 years :
• Son = y - 10
• Father = x - 10
It is given that before ten yrs the age of father was 2 times the age of his son.
So,
it becomes : (y - 10)2 = x - 10.
To get the value of x.
(y - 10)2 = x - 10
x - 10 = 2(y - 10)
x = 2y - 20 + 10
» x = 2y - 10 ____[ eq. I ]
Since x is 2y - 10 acc. to eq. i.
Their ages after 10 years :
• Father = x + 10
• Son = y + 10
Their ages after 10 years comes in the ratio of 14 : 9.
________(given).
so, from this all we got an another equation :
x + 10/ y + 10 =14/9 ____[eq. ii]
Solution :
x + 10/ y + 10 =14/9
{Subtituting the value of eq. I in eq. ii : x = 2y - 10}
(2y - 10) + 10/ y + 10 = 14/9
2y/ y + 10 = 14/9
(2y)9 = (y + 10)14
18y = 14y + 140
18y - 14y = 140
» y = 35
We got the age of the son (y) that is 35 yrs.
Father's age :
2y - 10
= 60 yrs.
Verification :
we know that before 10 years the age of father was 2 times the age of son.
age of his dad before 10 yrs=50
Son's age before 10 yrs = 25
50 is 2 times of the 25.
______Verified.
:)