12
Q:

# Five years ago, the average age of A, B, C and D was 45 years. With E Joining them now, the average of all the five is 49 years. The age of E is?

Q:

Ten years ago, A was half of B in age. If the ratio of their present ages is 3:4, then what will be the total of their present ages?

Let A's age 10 years ago be x years . Then B's age 10 years ago be 2x years

$\inline \fn_cm \Rightarrow \frac{x+10}{2x+10}=\frac{3}{4}$

$\inline \fn_cm \Rightarrow4(x+10)=3(2x+10)$

$\inline \fn_cm \Rightarrow x=5$

$\inline \fn_cm \therefore$ Total of their present ages = x + 10 + 2x + 10

= 3x+20

= 3 * 5 + 20 = 35 years

270
Q:

The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years. The ratio of number of boys to the number of girls in the class is

Suppose the number of boys and girls are x and y respectively

$\inline \fn_cm \Rightarrow \frac{x\times 16.4 + y\times 15.4}{x+y}=15.8$

$\inline \fn_cm \Rightarrow 16.4x + 15.4y = 15.8x+15.8y$

$\inline \fn_cm \Rightarrow0.6x=0.4y$

$\inline \fn_cm \therefore \frac{x}{y}=\frac{0.4}{0.6}=\frac{2}{3}=2:3$

797
Q:

The ratio of the father's age to the son's age is 3 : 1. The product of their ages is 147. The ratio of their ages after 5 years will be?

Let father's age be 3x and son's age be x years

$\inline \fn_cm \Rightarrow 3x\times x=147$

$\inline \fn_cm \Rightarrow x^{2}=49\Rightarrow x=7$

Father's age after 5 years = 3x + 5 = 26 years

Son's age after 5 years = x + 5 = 12 years

$\inline \fn_cm \therefore$ Ratio of father's and son's ages = 26 : 12 = 13 : 6

514
Q:

The average age of a couple was 26 years at the time of marriage. After 11 years of marriage, the average age of the family with 3 children become 19 years. The average age of the children is

The average age of a couple = 26 years.

Total age of couples = 26 x 2 = 52 years

$\inline \fn_cm \therefore$ Total age of couple after 11 years = (52 + 2 * 11 ) = 74 years

Suppose average age of 3 children after 11 years is 3x years.

$\inline \fn_cm \Rightarrow \frac{74+3x}{5}=19 \Rightarrow x=7$

The average age of children is 7 years.

384
Q:

The average age of a group of 10 students is 15 years. When 5 more students join the group, the average age increase by 1 year. The average age of the new student is?

Total age of 10 students = 150 years

Total age of 15 students = 240 years

Total age of 5 new students = 240 - 150 = 90 years

$\inline \fn_cm \therefore$ Average age of 5 new students = 90/5 = 18 years.