The average age of 4 members of a family is 35 years. Their ages are in the ratio $8:7:1:12$. What is the age of the oldest member of the family (in years)?

Number of members = 4Average age = 35 yearsSum of ages of all members = $4\times 35=140$ yearsThe ratio of their ages is $8:7:1:12$.Let their ages be $8x,7x,x,\text{ and }12x$.Sum of ratios = $8x+7x+x+12x=28x$ $
$28x=140$ $
$$x=\frac{140}{28}=5$$
The ratio value for the oldest member is 12.Age of the oldest member = $12x=12\times 5=60$ years.