Q. A, B, C, D, are four friends. Average age of A and C is 35 years and that of B, and D is 40 years. Average age of B, C and D is 40 years. The sum of the ages of A and D is equal to that of B and C. Find out the ages (in years) of A, B, C and D.
✅ Correct Answer: (C)
30, 35, 40, 45
Explanation: Given :- Average age of A and C = 35 years
⇒ A + C = 70 years ......... ( ⅰ )
Average age of B, and D = 40 years.
⇒ B + D = 80 years ......... ( ⅱ )
and Average age of B, C and D = 40 years.
⇒ B + C + D = 120 years ......... ( ⅲ )
With the help of equations ( ⅰ ) , ( ⅱ ) and ( ⅲ ) , we get
∴ age of C = 40 years and age of A = 30 years
According to question ,
∴ age of A + age of D = age of B + age of C
⇒ A + D = B + C
⇒ 30 + D = B + 40 ⇒ D – B = 10
∴ age of B = 35 years and age of D = 45 years
Explanation by: Siddharth M
Given :- Average age of A and C = 35 years
⇒ A + C = 70 years ......... ( ⅰ )
Average age of B, and D = 40 years.
⇒ B + D = 80 years ......... ( ⅱ )
and Average age of B, C and D = 40 years.
⇒ B + C + D = 120 years ......... ( ⅲ )
With the help of equations ( ⅰ ) , ( ⅱ ) and ( ⅲ ) , we get
∴ age of C = 40 years and age of A = 30 years
According to question ,
∴ age of A + age of D = age of B + age of C
⇒ A + D = B + C
⇒ 30 + D = B + 40 ⇒ D – B = 10
∴ age of B = 35 years and age of D = 45 years
⇒ A + C = 70 years ......... ( ⅰ )
Average age of B, and D = 40 years.
⇒ B + D = 80 years ......... ( ⅱ )
and Average age of B, C and D = 40 years.
⇒ B + C + D = 120 years ......... ( ⅲ )
With the help of equations ( ⅰ ) , ( ⅱ ) and ( ⅲ ) , we get
∴ age of C = 40 years and age of A = 30 years
According to question ,
∴ age of A + age of D = age of B + age of C
⇒ A + D = B + C
⇒ 30 + D = B + 40 ⇒ D – B = 10
∴ age of B = 35 years and age of D = 45 years