Question

There are 60 persons. The age of each person

(in years) is a two digit number. The average age of

the persons is A years. One of the persons whose

age is ‘ab’ is replaced by a new person whose age

is ‘ba’. If the average age of the new group is

0.8A years. Find the maximum value of A.

(A) 12 (B) 10.8

(C) 11.4 (D) Data inconsistent​

Answer 1

Answer:

c

Step-by-step explanation:

i hoped to help you thanks.

Answer 2

The maximum value of A is 6.

Given:

Number of people = 60

Average age = A years

Removed age = ab years

Added age = ba years

Average age of new group = 0.8A years

To find: Maximum value of A

Solution:

We know that,

Average age = $\frac{sum-of-ages-of-people}{number-of-people}$

⇒ sum of ages of people/60 = A [according to given]

⇒ sum of ages of people = 60A

Now,

Removed age = ab years = 10a + b years [place value]

Added age = ba years = 10b + a years [place value]

New sum = Old sum - removed age + added age

⇒ New sum = 60A - (10a +b) + (10b + a)

⇒ New sum = 60A + 9(b - a)

⇒ New average = $\frac{60A + 9(b - a)}{60}$

⇒ New average = A + $\frac{3(b-a)}{20}$

We know that,

New average = 0.8A

⇒ A + $\frac{3(b-a)}{20}$ = 0.8A

⇒ 0.2A = $\frac{3(a-b)}{20}$

⇒ A = $\frac{3(a-b)}{4}$

Now,

a and b are single-digit numbers

⇒ Maximum value of (a-b) such that ab and ba are two-digit numbers would be the maximum value of (a-b) such that a and b are non-zero

⇒ Maximum value of (a-b) = 9-1 = 8

⇒ Maximum value of  $\frac{3(a-b)}{4}$ = 6

⇒ Max value of A = 6

SPJ2