Question : The average age of four members of a family is 32 years. If the age of a guest is included, then the average age increases by 12.5%. What is the age (in years) of the guest?
Option 1: 52
Option 2: 56
Option 3: 44
Option 4: 12
Correct Answer: 52
Solution :
Given that the average age of four members of a family is 32 years.
⇒ Sum of age of 4 members = 32 × 4 = 128
Now, if the age of the guest is included, the average increases by 12.5%.
Let the age of the guest be $x$.
Now, the total number of members = 5
⇒ New average = 112.5% of 32
⇒ $\frac{\text{Sum of age of 4 members }+\ x}{5}=\frac{112.5}{100}\times 32$
⇒ $\frac{128 + x}{5}=36$
⇒ $128+x=36\times 5$
⇒ $x=180-128$
$\therefore x=52$ years
Hence, the correct answer is 52.
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