Question

One year ago the ratio between samir and ashok's age was 4:3. one year hence the ratio of their age will be 5:4. what is the sum of their present ages in years?

Answer 1

Let the present age of samir be X.
Let the present age of ashok be Y.
=> Age of samir one year back = X-1.
=> Age of ashok one year back = Y-1.
And, Age of samir after one year = X+1.
And, Age of Ashok after one year = Y+1.
Ratio of samir's and ashok's ages one year back = 4:3.
=> X-1/Y-1 = 4/3
     3X-3 = 4Y-4
     3X-4Y= -1   -------------> 1
Ratio of samir's and ashok's ages after one year = 5:4.
=> X+1/Y+1 = 5/4
     4X+4 = 5Y+5
     4X-5Y = 1 -----------------> 2
Solving 1 and 2, we get
X=9 and Y=7.

Answer 2

Samir is 9 years and Ashok is 7 years, now the sum of their present ages is 16.

What is the formula of age problem?

• Important Statements and Equations for "Problems based on Ages".
• If the present age is y, then n times the present age = ny.
• If the present age is x, then age n years later/hence = x + n.

How do you answer age problems?

• Create an equation based on the information provided.
• Solve for the unknown variable.
• Substitute our answer back into the equation to see if the left side of the equation equals the right side of the equation.

According to the question:

Let the ages of Samir and Ashok be S and A, now.

(S-1):(A-1)= 4:3, or

4(A-1) = 3(S-1), or

4A= 3S-3+4 = 3S+1 …..............(1)

(S+1):(A+1)= 5:4, or

5(A+1) = 4(S+1), or

5A= 4S+4 -5= 4S-1 …...............(2)

From (1), 20A = 15S+5 …..........(3)

From (2), 20A = 16S-4 …..........(4)

Equate (3) and (4).

15S+5 = 16S-4.

16S-15S=5+4, or

S = 9.

From (2), 5A = 36–1 = 35, or

A = 7,

Hence, Samir is 9 years and Ashok is 7 years, now the sum of their present ages is 16.

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