Question

if the sum of father age and his sun in year 65 amd twice difference of their years is 50,then the age of father is
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Answer 1

Step-by-step explanation:

Given:-

• The sum of ages of father and son is 65 years.

• Twice the difference of their ages is 50.

To Find:-

• The present age of father.

Solution:-

Let the present age of father be x

And present age of son be y

Case 1:-

Age of father + Age of son = 65

$\sf \implies x + y = 65......(i)$

Case 2:-

2(Father's age - Son's age) = 50

$\sf \implies 2(x - y)= 50$

$\sf \implies x - y = \dfrac{50}{2}$

$\sf \implies x - y = 25......(ii)$

Adding equation (i) and (ii)

$\sf \implies x + y + x - y = 65 + 25$

$\sf \implies 2x = 90$

$\sf \implies x = \dfrac{90}{2}$

$\sf \implies x = 45$

Substitute x = 45 in equation (i)

$\sf \implies x + y = 65$

$\sf \implies 45 + y = 65$

$\sf \implies y = 65 - 45$

$\sf \implies y = 20$

We have:-

• x = 45 = Present age of father

• y = 20 = Present age of son

$\underline{\boxed{\sf \therefore The \: present \: age \: of \: father = 45 \: years}}$

Answer 2

Given:-

◈Sum of age of Father a d his sun = 65yrs

◈Twice of difference between thir ages = 50yrs

Find:-

◈Age of Father

Solution:-

❏Let, Age of Father be 'x' yrs

❏Age of Son be 'y' yrs

$\qquad$ ❝$\underline{\pink{\sf According \:To \:Question}}$❞

＊$\purple{\bf{Sum \:of\: their\:ages\:is\:65}}$

⇰$\bf{x+y = 65}\large{.........eq.1}$

$\ast\orange{\bf{Twice\:of\:diff.\: between\:their\:ages\:is\:50}}$

⇰$\bf{2(x-y) = 50}\large{.........eq.2}$

〘 $\bf{Taking\:Eq.}$➊〙

➨$\blue{\sf x + y = 65}$

➨$\blue{\sf x = 65-y}$

【$\bf{Using\:value\:of\:x\:in\:eq.2}$】

➠$\purple{\sf 2(x-y) = 50}$

➠$\purple{\sf 2\bigg\lgroup{\sf 65-y- y}\bigg\rgroup = 50}$

➠$\purple{\sf 2\bigg\lgroup{\sf 65-2y}\bigg\rgroup = 50}$

➠$\purple{\sf 130-4y= 50}$

➠$\purple{\sf -4y= 50-130}$

➠$\purple{\sf -4y= -80}$

➠$\purple{\sf y= \dfrac{-80}{-4}}$

➠$\purple{\sf y= 20yrs}$

『$\bf{Using\:value\:of\:y\:in\:eq.1}$』

➫$\pink{\sf x+y = 65}$

➫$\pink{\sf x+(20) = 65}$

➫$\pink{\sf x+20 = 65}$

➫$\pink{\sf x = 65-20}$

➫$\pink{\sf x = 45yrs}$

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Hence,

• Father's Present Age = x = 45yrs
• Son's Present Age = y = 20yrs

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