David’s present age is 2/7th of his father’s present age. David’s brother is three year older to James. The respective ratio between present ages of David father and David’s brother is 14:5. What is the present age of David?
(a) 12 years
(b) 23 years
(c) 19 years
(d) 27 years
(e) 13 years
Answer: (a)
David’s father present age = x
David’s age = \(\displaystyle \frac{2}{7}x\)
David’s brother age = \(\displaystyle \frac{2}{7}x+3\)
\(\displaystyle \frac{x}{{\frac{2}{7}x+3}}=\frac{{14}}{5}\)
x = 42
David’s age = \(\displaystyle \frac{2}{7}x=\frac{2}{7}\times 42=12\)
If average of 20 observations \(\displaystyle {{x}_{1}},{{x}_{2}},…..{{x}_{{20}}}\) is y, then the Average of \(\displaystyle {{x}_{1}}-101,{{x}_{2}}-101,{{x}_{3}}-101,…..{{x}_{{20}}}-101\) is
Required average
\(\displaystyle \begin{array}{l}=\frac{{{{x}_{1}}-101+{{x}_{2}}-101+….+{{x}_{{20}}}-101}}{{20}}\\=\frac{{({{x}_{1}}+{{x}_{2}}+….+{{x}_{{20}}})-20\times 101}}{{20}}\\=\frac{{20y-20\times 101}}{{20}}\\=y-101\end{array}\)
A library has an average number of 510 visitors on Sunday and 240 on other days. The average number of visitors per day in a month of 30 days beginning with Sunday is :
(a) 285
(b) 295
(c) 300
(d) 290
(e) 320
Answer: (a)
That month will have 5 Sundays
Required average = \(\displaystyle \frac{{5\times 510+25\times 240}}{{30}}\)
\(\displaystyle \frac{{2500+6000}}{{30}}=\frac{{8550}}{{30}}=285\)
The average monthly expenditure of a family is ₹ 2,200 during first three months, ₹ 2,550 during next four months and ₹ 3,120 during last five months of the year. If the total savings during the year was ₹ 1,260 what is the average monthly income?
(a) ₹ 1,260
(b) ₹ 1,280
(c) ₹ 2,805
(d) ₹ 2,850
(e) ₹ 2,500
Answer: (c)
Total expenditure of the year = (3 × 2200 + 4 × 2550 + 5 × 3120)
= (6600 + 10200 + 15600) = 32400
Total income of the year = (32400 + 1260) = 33660
Average monthly income = \(\displaystyle \frac{{33660}}{{12}}=2805\)
4 boys and 3 girls spent ₹ 120 on the average, of which boys spent ₹ 150 on the average. Then the average amount spent by the girls is
(a) ₹ 80
(b) ₹ 60
(c) ₹ 90
(d)₹ 100
(e)₹ 120
Answer: (a)
Total expenditure = 120 × 7 = Rs. 840
Total expenditure of 4 boys = 150 × 4 = ₹ 600
Total expenditure of 3 girls
= 840 – 600 = ₹ 240
Their average expenditure = \(\displaystyle \frac{{240}}{3}=80\)
