If A’s age is reduced by 5 years and B’s age is increased by 3 yea

1.	If A’s age is reduced by 5 years and B’s age is increased by 3 years, then the product of their ages is reduced by 9. If we increase A’s age by 3 years and B’s age by 2 years, then the product of their ages is increased by 67. Find the ages of A and B.1. 17, 92. 15, 83. 13, 74. 19, 10
Answer» Correct Answer - Option 1 : 17, 9 Given∶ A’s age is reduced by 5 years and B’s age is increased by 3 years, then the product of their ages is reduced by 9. Also, if we increase A’s age by 3 years and B’s age by 2 years, then the product of their ages is increased by 67. Formula Used∶ Concept of Linear Equations, Elimination Method. Calculation∶ Let the ages of A and B be ‘x’ and ‘y’ years. Then the product of their ages = xy According to question, (x - 5)(y + 3) = xy – 9 ⇒ 3x – 5y – 6 = 0 ----(1) Also, (x + 3)(y + 2) = xy + 67 ⇒ 2x + 3y - 61 = 0 ----(2) On multiplying eq.(1) by 2 and eq.(2) by 3, we get 6x – 10y – 12 = 0 ----(3) 6x + 9y – 183 = 0 ----(4) Subtracting eq. (3) from (4), we get 19y – 171 = 0 ⇒ y = 9 Substitute the value of y = 9 in eq.(2), we get 2x + 3(9) – 61 = 0 ⇒ 2x + 27 – 61 = 0 ⇒ 2x = 34 ⇒ x = 17 Hence, A’s age is 17 years and B’s age is 9 years.

If A’s age is reduced by 5 years and B’s age is increased by 3 years, then the product of their ages is reduced by 9. If we increase A’s age by 3 years and B’s age by 2 years, then the product of their ages is increased by 67. Find the ages of A and B.1. 17, 92. 15, 83. 13, 74. 19, 10

Answer» Correct Answer - Option 1 : 17, 9

Given∶

A’s age is reduced by 5 years and B’s age is increased by 3 years, then the product of their ages is reduced by 9.

Also, if we increase A’s age by 3 years and B’s age by 2 years, then the product of their ages is increased by 67.

Formula Used∶

Concept of Linear Equations, Elimination Method.

Calculation∶

Let the ages of A and B be ‘x’ and ‘y’ years.

Then the product of their ages = xy

According to question,

(x - 5)(y + 3) = xy – 9

⇒ 3x – 5y – 6 = 0 ----(1)

Also, (x + 3)(y + 2) = xy + 67

⇒ 2x + 3y - 61 = 0 ----(2)

On multiplying eq.(1) by 2 and eq.(2) by 3, we get

6x – 10y – 12 = 0 ----(3)

6x + 9y – 183 = 0 ----(4)

Subtracting eq. (3) from (4), we get

19y – 171 = 0

⇒ y = 9

Substitute the value of y = 9 in eq.(2), we get

2x + 3(9) – 61 = 0

⇒ 2x + 27 – 61 = 0

⇒ 2x = 34

⇒ x = 17

Hence, A’s age is 17 years and B’s age is 9 years.