Math, asked by sushant125098, 9 months ago

Help plz.

"I am five times as old as you were, when I was as old as you are", said a man to his son. Find out their present ages, if the sum of their ages is 64 years?

Answers

Answered by Anonymous

49

REQUIRED SOLUTION

Father's Present Age = x
Son's Present Age = y

Now father tells that he was of y age and his son was of age y-(x-y).

So x+y=64

x = 5[y-(x-y)]

x = 5[y-x+y]

x = 5[2y-x]

x = 10y-5x

x + 5x = 10y

6x = 10y

x = 10y / 6

10y / 6 + y = 64

10y / 6 + 6y / 6 = 64

16y = 64 * 6

16y = 384

y = 384 / 16

y = 24 = Son's Age

x+24=64

x=64-24

x = 40= Father's Age

y - (x-y) = 24 - (40-24)

= 24 - 16 = 8

Thank You ✌

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Answered by Anonymous

21

Given :

Man was 5 times as old as his son when man was son's age.
Sum of the age of man and son is 64 years.

To Find :

Present age of man
Present age of son

Solution :

Let the present age of man be x years.

Let the present age of son be y years.

Case 1 :

➣ $\mathtt{x=5\:\big[y\:-\:(x-y)\big]}$

➣ $\mathtt{x=5\:\big[y-x+y\big]}$

➣ $\mathtt{x=5\:\:(2y-x) }$

➣ $\mathtt{x=10y-5x}$

➣ $\mathtt{x+5x=10y}$

➣ $\mathtt{6x=10y}$

$\mathtt{x={\dfrac{10y}{6}}}$ ____(1)

Case 2 :

➣ $\mathtt{Man\:+\:son\:=\:64}$

$\mathtt{x+y=64}$ ___(2)

★ Substitute, x = 10y/6 from equation (1),

➣ $\mathtt{\dfrac{10y}{6}\:+\:y\:=64}$

➣ $\mathtt{\dfrac{10y+6y}{6}\:=64}$

➣ $\mathtt{\dfrac{16y}{6}=64}$

➣ $\mathtt{16y=64\:\times\:6}$

➣ $\mathtt{16y=384}$

➣ $\mathtt{y={\dfrac{384}{16}}}$

➣ $\mathtt{y=24}$

★ Substute, y = 24 in equation (2),

➣ $\mathtt{x+y=64}$

➣ $\mathtt{x=64-y}$

➣ $\mathtt{x=64-24}$

➣ $\mathtt{x=40}$

★ Present age :

$\large{\boxed{\sf{\blue{Present\:age\:of\:man\:=\:x\:=\:40\:years}}}}$

$\large{\boxed{\sf{\blue{Present\:age\:of\:son\:=\:y\:=\:24\:years}}}}$

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