Suppose that the Ravi present age is A years.
According to the given question,
A/4 + A/5 + A/3 + 13 = A
Solve the above equation to find the answer.

Correct Option: C

Suppose that the Ravi present age is A years.
According to the given question,
A/4 + A/5 + A/3 + 13 = A
⇒ (15A + 12A + 20A)/60 = A - 13
⇒ 47A = 60A - 780
⇒60A - 47A = 780
⇒13A = 780
∴ A = 780/13 = 60 years

Let us assume the certain Number is A.
According to question,
63A = 3834 + 36A
Solve the equation.

Correct Option: C

Let us assume the certain Number is A.
According to question,
63A = 3834 + 36A
63A - 36A = 3834
⇒ 27A = 3834
⇒ A = 142

Let us assume the digits of the original number are unit's digit a and ten's digit b.
The Original Number will be 10a + b.
After interchanging the digits the new number will be 10b + a.
According to question,
The number obtained by interchanging the two digits of a two-digit number is lesser than the original number by 54.
New Number = Original Number - 54
10b + a = 10a + b - 54
⇒ 10b + a - 10a - b = -54
⇒ 9b - 9a = -54
⇒ a - b = 6....................................(1)
Again according to question,
Sum of the digits of original number = 10
a + b = 10..................................................(2)

Solve the equation (1) and (2) and get the answer.

Correct Option: C

Let us assume the digits of the original number are unit's digit a and ten's digit b.
The Original Number will be 10a + b.
After interchanging the digits the new number will be 10b + a.
According to question,
The number obtained by interchanging the two digits of a two-digit number is lesser than the original number by 54.
New Number = Original Number - 54
10b + a = 10a + b - 54
⇒ 10b + a - 10a - b = -54
⇒ 9b - 9a = -54
⇒ a - b = 6....................................(1)
Again according to question,
Sum of the digits of original number = 10
a + b = 10..................................................(2)
Add the equation (1) and (2), we will get
a - b + a + b = 10 + 6
2a = 16
a = 8
Put the value of a in Equation (2) , we will get
8 + b = 10
b = 10 - 8
b = 2
Put the value of a and b for original number, we will get
10a + b = 10 x 8 + 2 = 80 + 2 = 82

Let us assume the present age of father = F year and Son's present age = S years
According to question, 5 years ago,
Father's age = F - 5 and Son's age = S - 5.
According to the question,
The age of the father 5 years ago was 5 times the age of his son.
F - 5 = 5(S - 5)
F - 5 = 5S - 25.....................(1)
At present the father's age is 3 times that of his son.
F = 3S.................................(2)
Solve the Equation and get the result.

Correct Option: B

Let us assume the present age of father = F year and Son's present age = S years
According to question, 5 years ago,
Father's age = F - 5 and Son's age = S - 5.
According to the question,
The age of the father 5 years ago was 5 times the age of his son.
F - 5 = 5(S - 5)
F - 5 = 5S - 25.....................(1)
At present the father's age is 3 times that of his son.
F = 3S.................................(2)
Put the value of F from equation (2) in equation (1), we will get
⇒ 3S - 5 = 5S - 25
⇒ 25 - 5 = 5S - 3S
⇒ 20 = 2S
⇒ 10 = S
⇒ S = 10.
Put the value of S in Equation (2). we will get,
F = 3S = 3 x 10 = 30
So the present Age of Father = 30.

2x + 3y = 29 ...(i)
and y = x + 3 ...(ii)
Putting the value of y from Eq. (ii) to Eq. (i), we get
2x + 3y = 29
2x + 3(x + 3) = 29

Correct Option: A

2x + 3y = 29 ...(i)
and y = x + 3 ...(ii)
Putting the value of y from Eq. (ii) to Eq. (i), we get
2x + 3y = 29
2x + 3(x + 3) = 29
2x + 3x + 9 = 29
⇒ 5x = 20
∴ x = 4