The sum of the ages of 4 members of a family 5 years ago was 94 years. Today, when the daughter has been married off and replaced by a daughter-in-law, the sum of their ages is 92. Assuming that there has been no other change in the family structure and all the people are alive, what is the difference in the age of the daughter and the daughter-in-law?
(a) 22 years
(b) 11 years
(c) 25 years
(d) 19 years
(e) 15 years
Answer: (a)
Let the 4 members are \(\displaystyle {{x}_{1}},{{x}_{2}},{{x}_{3}}\) , daughter
Sum of 4 members five years ago = \(\displaystyle {{x}_{1}}+{{x}_{2}}+{{x}_{3}}+daughter=94\)
After 5 years,
\(\displaystyle {{x}_{1}}+{{x}_{2}}+{{x}_{3}}+daughter=114\) …(1)
Daughter + daughter in law = 92
Daughter = 92 – daughter in law
Put this eqn. …(1)
\(\displaystyle {{x}_{1}}+{{x}_{2}}+{{x}_{3}}+92-daughterinlaw=114\)
\(\displaystyle {{x}_{1}}+{{x}_{2}}+{{x}_{3}}=22+daughterinlaw\)
So, the required difference is 22 years.
The average score of a cricketer for 13 matches is 42 runs. If his average score for the first 5 matches is 54, then what is his average score (in runs) for last 8 matches?
(a) 37
(b) 39
(c) 34.5
(d) 33.5
(e) 37.5
Answer: (c)
Let \(\displaystyle {{M}_{1}},{{M}_{2}},{{M}_{3}},……….{{M}_{{13}}}\) are matches played by cricket players
\(\displaystyle \frac{{{{M}_{1}}+{{M}_{2}}+{{M}_{3}}+{{M}_{4}}+{{M}_{5}}+{{M}_{6}}+{{M}_{7}}+{{M}_{8}}+{{M}_{9}}+{{M}_{{10}}}+{{M}_{{11}}}+{{M}_{{12}}}+{{M}_{{13}}}}}{{13}}=42\) ….(1)
\(\displaystyle \frac{{{{M}_{1}}+{{M}_{2}}+{{M}_{3}}+{{M}_{4}}+{{M}_{5}}}}{5}=54\) … (2)
From eqn. (1) and (2)
\(\displaystyle 270+{{M}_{6}}+{{M}_{7}}+{{M}_{8}}+{{M}_{9}}+{{M}_{{10}}}+{{M}_{{11}}}+{{M}_{{12}}}+{{M}_{{13}}}=42\times 13=546\)
or, \(\displaystyle \frac{{{{M}_{6}}+{{M}_{7}}+{{M}_{8}}+{{M}_{9}}+{{M}_{{10}}}+{{M}_{{11}}}+{{M}_{{12}}}+{{M}_{{13}}}}}{8}=\frac{{276}}{8}=34.5\)
The respective ratio between the present ages of son, mother, father and grandfather is 2 : 7 : 8 : 12. The average age of son and mother is 27 yr. What will be mother’s age after 7 yr?
(a) 40 yr
(b) 41 yr
(c) 48 yr
(d) 49 yr
(e) None of these
Answer: (d)
Total age of son and mother
2x + 7x = 2 × 27
9x = 54
x = 6
Mother’s age after 7 yr = 7x + 7 = 7 × 6 + 7 = 49 yr
The average height of 16 students is 142 cm. If the height of the teacher is included, the average height increases by 1 cm. The height of the teacher is
(a) 156 cm
(b) 159 cm
(c) 158 cm
(d) 157 cm
(e) 159.5 cm
Answer: (b)
Total height of 16 students= 16 × 142 cm = 2272 cm
Let height of teacher be x.
\(\displaystyle \frac{{2272+x}}{{17}}=143\)
2272 + x = 2431
x = 2431 – 2272 = 159
Height of teacher is 159 cm
The average marks obtained by 100 candidates in an examination are 45. If the average marks of the passed students are 50 while the average marks of the failed students is 40. Then find the number of students who passed the examination.
(a) 30
(b) 40
(c) 50
(d) 60
(e) None of these
Answer: (c)
Let P = passed students and failed students = F. So
45 × 100 = 50 × P + 40 × F and P + F = 100. Solve for F and P, we will get P = 50.
The average age of 80 girls was 20 years, the average age of 20 of them was 22 years and that of another 20 was 24 years. Find the average age of the remaining girls.
(a) 17 years
(b) 19 years
(c) 21 years
(d) 15 years
(e) None of these
Answer: (a)
Total age of remaining 40 girls
= (80 × 20 – 20 × 22 – 20 × 24) years
= (1600 – 440 – 480) years
= 680 years
Therefore, Required average age = \(\displaystyle \frac{{680}}{{40}}=17years\)
