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MAT Exam 2021 Paper

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Question : 86 of 200

Marks: +1, -0

If the ages of

P

R

are added to twice the age of

Q

, the total becomes 59 . If the ages of

Q

R

are added to thrice the age of

P

, the total becomes 68 and if the age of

P

is added to thrice the age of

Q

and thrice the age of

R

, the total becomes 108. What is the age of

P

?

19 year
15 year
17 year
12 year

Solution:

Concept:

Form linear equations from the given conditions and solve them to find the value of

P

.

Explanation:

Let the ages of

P

,

Q

, and

R

be

P

,

Q

, and

R

respectively.

From the first condition:

P + 2Q + R = 59 \quad \cdots (1)

From the second condition:

3P + Q + R = 68 \quad \cdots (2)

From the third condition:

P + 3Q + 3R = 108 \quad \cdots (3)

Multiply equation

(2)

by

3

:

9P + 3Q + 3R = 204

Subtract equation

(3)

from this equation:

(9P - P) + (3Q - 3Q) + (3R - 3R) = 204 - 108

8P = 96

P = 12

Thus, the age of

P

is

12

years.

Answer:

D. 12 year

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