Question

The sum of the ages of anup and his father is 100.when anup is as old as his father now,he will be five times as old as his son anuj is now.anuj will be eight years older than anup is now when anup is as old as his father, what are their ages now?

Answer 1

AnswEr :

$\bf{\large{\underline{\sf{Given\::}}}}$

The sum of the ages of Anup and his father is 100. When Anup is as old as his father now, he will be five times as old as his son Anuj is now, Anuj will be eight years older than Anup is now when Anup is old as his father.

$\bf{\large{\underline{\sf{To\:find\::}}}}$

Their Ages now.

$\bf{\Large{\underline{\rm{\purple{Explanation\::}}}}}$

Let Anup's age be R years

Let Anup's father age be (100 - R) years

Let Anuj's age be $\sf{\dfrac{100-R}{5} }$ years

$\bf{\Large{\underline{\underline{\tt{\red{A.T.Q\::}}}}}}$

$\longrightarrow\tt{(R+8)=(100-R)-R+\dfrac{100-R}{5} }\\\\\\\\\longrightarrow\tt{R+8=100-2R+\dfrac{100-R}{5} }\\\\\\\\\longrightarrow\tt{R+8=\dfrac{500-10R+100-R}{5} }\\\\\\\\\longrightarrow\tt{5R+40=500-10R+100-R}\\\\\\\\\longrightarrow\tt{5R+40=600-11R}\\\\\\\\\longrightarrow\tt{5R+11R=600-40}\\\\\\\\\longrightarrow\tt{16R=560}\\\\\\\\\longrightarrow\tt{R=\cancel{\dfrac{560}{16}} }\\\\\\\\\longrightarrow\tt{\red{R\:=\:35\:years}}$

Now,

$\bullet\sf{Anup's\:age\:is\:=35\:years}\\\\\bullet\sf{Anup's\:father's\:age\:is\:(100-35)=65\:years}\\\\\bullet\sf{Anuj's\:age\:is\:\dfrac{100-35}{5} =\cancel{\dfrac{65}{5}} =13\:years}}$

Answer 2

Answer:

Anup's age = 35 Years

Father's age = 65 Years

Anuj's age = 13 Years

Step by step explanation:

Given: As in the question

• The sum of ages of Anup and his father is 100.

• When Anup is as old as his father now, he will be five times as old as his son Anuj is now. Anuj will be eight years older than Anup now, when Anup is as old as his father.

To find: Present ages of Anuj , Anup and Father

:- According to the question

Let present age of Anup be x years

→ Present age of his father (100–x ) years

Condition 1

When Anup's age = His father's age = 5 x Anuj's present age

$\large\implies{\sf }$ 100–x = Anuj's present age

∴ Anuj's present age = (100–x)/5

Condition 2

When Anup is as old as his father now

When Anup is as old as his father now after (100–x)–x years Anuj's age is equal to his father's present age + 8

$\large\implies{\sf }$ Present age of Anuj + (100–2x) = Present age of Anup + 8

Therefore,

$\large\implies{\sf }$(100–x)/5 + (100– 2x) = X + 8

$\large\implies{\sf }$ 100–x + 5 (100–2x) = 5(x + 8)

$\large\implies{\sf }$ 100–x +500 –10x = 5x + 40

$\large\implies{\sf }$ –11x –5x = 40 – 600

$\large\implies{\sf }$ –16x = –560

$\large\implies{\sf }$ x = (–560/ –16)

$\large\implies{\sf }$ 35

∴Anup's present age = 35 Years

∴Father's present age = (100–x) = (100–35) = 65 years

∴ Anuj's present age = (100– x)/5 = (100–35)/5 = 13 Years