Ram's age = 20 years and Shyam's age = 25. Do this with keeping the topic pair of linear equation in two variable
Answers
Answer:
Hint: We will take Ram’s present age as a variable and form linear equations using the data given in questions. Then we will solve these equations to find the value of the variable.
Complete step-by-step answer:
Let us consider the Ram's present age to be
x
x
.
Then, since Ram's age is half of his father’s age. His father’s age will be double the age of Ram.
Therefore, his father’s age will be
2x
2x
.
Now, let us consider their ages 20 years ago.
20 years ago, their ages will be 20 years less than their present age.
Therefore, Ram’s age 20 years ago will be
=x−20
=x−20
years.
And Ram’s father’s age 20 years ago will be
=2x−20
=2x−20
years.
Now, according to question, 20 years ago Ram’s father’s age was 6 times that of Ram’s age.
Therefore, using above data, we get,
2x−20=6
(
x−20)
2x−20=6(x−20)
Applying distributive law, we get,
2x−20=6x−120
2x−20=6x−120
Subtracting
2x
2x
from both sides of the equation, we get,
2x−20−2x=6x−120−2x
⇒4x−120=−20
2x−20−2x=6x−120−2x⇒4x−120=−20
Adding 120 both sides of the equation, we get,
4x−120+120=−20+120
⇒4x=100
4x−120+120=−20+120⇒4x=100
Dividing 4 from both sides of the equation, we get,
x=
100
4
=25
x=1004=25
Hence, we get that, Ram’s present age is 25 years.
Therefore, his father’s present age will be
2×25=50
2×25=50
years.
Therefore, the correct answer is option (b).
Note: This question can also be solved taking fathers present age to be
x
x
. Also, you can take Ram’s or his father’s age 20 years ago to be
x
x
and then solve it. Answers will be the same with all approaches.