Q) Five years ago, Adil was thrice as old as Bharat. Ten years later Adil shall be twice as old as Bharat. To know the present ages of Adil and Bharat:
(i) form the linear equations representing the above information.
(ii) show that the system of equations is consistent with unique solution.
(iii) find the present ages of Adil and Bharat.

(Q 32 B – 30/3/3 – CBSE 2026 Question Paper)

Ans:

Let’s consider Adil’s present age is X years and Bharat’s present age is Y years

Step 1: By 1st given condition, “Five years ago, Adil was thrice as old as Bharat.”

∴ X – 5 = 3 ( Y – 5)

∴ X – 5 = 3 Y – 15

∴ X – 3 Y = – 15 + 5 

X – 3 Y = – 10 ……… (i)

Step 2: By 2nd given condition, “Ten years later Adil shall be twice as old as Bharat.”

∴ X + 10 = 2 ( Y + 10)

∴ X + 10 = 2 Y + 20

∴ X – 2 Y = 20 – 10 

∴ X – 2 Y = 10 ……… (ii)

Step 3: By subtracting equation (i) from equation (ii), we get:

∴ (X – 2 Y) – ( X – 3 Y) = 10 – (- 10)

∴ X – 2 Y – X + 3 Y = 10 + 10

∴ Y = 20

Step 4: By substituting value of Y in equation (ii), we get:

∴ X – 2 Y = 10

∴ X – 2 (20) = 10

∴ X = 10 + 40 

∴ X = 50

Therefore, present ages of Adil is 50 years and that of Bharat is 20 years.

Check: lets consider that Adil is 50 years and Bharat is 20 years
Now, 5 years ago, Adil’s age is 45 years and Bharat’s age is 15 years.
Since, 45 = 3 x 15, it matches with 1st condition.
Next, 10 years later, Adil’s age is 60 years and Bharat’s age is 30 years.
Since, 60 = 2 x 30, it matches with 2nd condition.
Since both given conditions are matched, our answer is correct.

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