Question

59. The ages of two persons differ by 20
years, if 5 years ago, the elder one
be 5 times as old as the younger one
Their present ages in years) are
respectively​

Answer 1

Answer:

let the age of elder one be X

age of younger one be X - 20

Step-by-step explanation:

5 years ago,

elder one age X - 5

younger one X -25

X-5=5(X -25)

X-5=5x-125

X -5x=-125+5

-4x =-120

X=120÷4

X = 30

elder one age =30

younger one age =10

Answer 2

Given :

• The ages of two persons differ by 20years.
• 5 years ago, the elder one
• be 5 times as old as the younger one.

To Find :

• Present age of elder one
• Present age of younger one.

Solution :

Let the present age of elder one be x years.

Let the present age of younger one be y years.

✪ Case 1 :

$\mathtt{Elder\:one\:-\:Younger\:one\:=\:20}$

$\mathtt{x-y=20}$ ____(1)

✪ Case 2 :

Given about ages 5 years ago,

• Elder one → (x-5) years
• Younger one →(y-5) years.

✪ Equation :

$\mathtt{Elder\:one\:=\:5(Younger\:one)}$

➣ $\mathtt{x-5=5(y-5) }$

➣ $\mathtt{x-5=5y-25}$

➣ $\mathtt{x-5y=-25+5}$

$\mathtt{x-5y=-20}$ ___(2)

✪ Solve equation 1 and 2 simultaneously and find the value of x and y.

✪ Subtract equation 2 from equation 1,

➣ $\mathtt{x-y-(x-5y)\:=\:20-(-20)}$

➣ $\mathtt{x-y-x+5y=20+20}$

➣ $\mathtt{4y=40}$

➣ $\mathtt{y\:=\:{\dfrac{40}{4}}}$

➣ $\mathtt{y=10}$

✪ Substite y = 10 in equation 1,

➣ $\mathtt{x-y=20}$

➣ $\mathtt{x=20+y}$

➣ $\mathtt{x=20+10}$

➣ $\mathtt{x=30}$

$\large{\boxed{\sf{\purple{Present\:age\:of\:elder\:one\:=\:x\:=\:30\:years}}}}$

$\large{\boxed{\sf{\purple{Present\:age\:of\:younger\:one\:=\:y\:=\:10\:years}}}}$