Solve the following MCQ on average questions for competitive exams:
Vikram scored 72 per cent marks in five subjects together, viz; Hindi, Science, Maths, English and Sanskrit together, where in the maximum marks of each subject were 100. How many marks did Vikram score in Science if he scored 80 marks in Hindi, 70 marks in Sanskrit, 76 marks in Maths and 65 marks in English?
(a) 72
(b) 69
(c) 59
(d) 71
(e) None of these
Answer: (b)
Let A = x, B = x + 1, C = x + 2, D = x + 3
Total number obtained by Vikram = \(\displaystyle (100\times 5)\times \frac{{72}}{{100}}=500\times \frac{{72}}{{100}}=360\)
Therefore, Number in science = 360 – (80 + 70 + 76 + 65) = 360 – 291 = 69
The average of four consecutive numbers A, B, C and D respectively is 56.5. What is the product of A and C?
(a) 3363
(b) 3306
(c) 3192
(d) 3080
(e) None of these
Answer: (e)
Let four consecutive numbers are
A = (x), B = (x + 1), C = (x + 2) and D = (x + 3)
According to question
Average = \(\displaystyle \frac{{(x)+(x+1)+(x+2)+(x+3)}}{4}\)
56.5 = \(\displaystyle \frac{{4x+6}}{4}\)
226 = 4x + 6
4x = 226 – 6 = 220
Therefore, x = \(\displaystyle \frac{{220}}{4}=55\)
\(\displaystyle \Rightarrow \) Product of A and C = (x) \(\displaystyle \times \)(x + 2)
= (55) \(\displaystyle \times \) (55 + 2) =55 \(\displaystyle \times \) 57 = 3135
The average of four consecutive odd numbers A, B, C and D respectively is 54. What is the product of A and C?
(a) 2907
(b) 2805
(c) 2703
(d) 2915
(e) None of these
Answer: (b)
Let four numbers be A, A + 2, A + 4, A + 6 A + A + 2 + A+ 4 + A + 6 = 54 × 4
4A + 12 = 216
4A = 216 – 12 = 204
Therefore, A = \(\displaystyle \frac{{204}}{4}=51\)
\(\displaystyle \Rightarrow \)B = A + 2 = 53
\(\displaystyle \Rightarrow \)C = A + 4 = 51 + 4 = 55
Therefore, D = A + 6 = 57
\(\displaystyle \Rightarrow \)A × C = 51 × 55 = 2805
The average age of a woman and her daughter is 19 years. The ratio of their ages is 16 : 3 respectively. What is the daughter’s age?
(a) 9 years
(b) 3 years
(c) 12 years
(d) 6 years
(e) None of these
Answer: (d)
Let Woman’s age = 16x
Daughter’s age = 3x
Now \(\displaystyle \frac{{(16x+3x)}}{2}=19\)
\(\displaystyle \Rightarrow \) 19x = 38
\(\displaystyle \Rightarrow \) x = 2
Therefore, Daughter’s age = 3 × 2 = 6 years
Average of five numbers is 61. If the average of first and third number is 69 and the average of second and fourth number is 69, what is the fifth number?
(a) 31
(b) 29
(c) 25
(d) 35
(e) None of these
Answer: (b)
Let the five no. Be \(\displaystyle {{x}_{1}},{{x}_{2}},{{x}_{3}},{{x}_{4}},{{x}_{5}}\)
Average of 5 numbers = 61
\(\displaystyle \frac{{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}+{{x}_{4}}+{{x}_{5}}}}{5}=61\)
\(\displaystyle {{x}_{1}}+{{x}_{2}}+{{x}_{3}}+{{x}_{4}}+{{x}_{5}}=305\)
Now, \(\displaystyle \frac{{{{x}_{1}}+{{x}_{3}}}}{2}=69\)
\(\displaystyle {{x}_{1}}+{{x}_{3}}=138\)
And also, \(\displaystyle \frac{{{{x}_{2}}+{{x}_{4}}}}{2}=69\)
\(\displaystyle {{x}_{2}}+{{x}_{4}}=138\)
Now, \(\displaystyle {{x}_{1}}+{{x}_{2}}+{{x}_{3}}+{{x}_{4}}+{{x}_{5}}=305\)
\(\displaystyle 138+138+{{x}_{5}}=305\)
\(\displaystyle {{x}_{5}}=305-276\)
\(\displaystyle {{x}_{5}}=29\)
