Numerical Reasoning (Arithmetic Series, Analogy, Classification, Arithmetical Reasoning, Fraction, Percentage, Ratio, Average, Profit & Loss, Time & Work, Date & Calendar, Data Sufficiency, Data Interpretation & Verification)

A can do a piece of work in 7 days of 9 hours each and B can do it in 6 days of 7 hours each. How long will they take to do it, working together 42/5 hours a day?
a) 1 day
b) 2 days
c) 3 days
d) 4 days

c) 3 days
Explanation: A can complete the work in 7 × 9 = 63 hours, so A’s 1 hour work = 1/63.
B can complete the work in 6 × 7 = 42 hours, so B’s 1 hour work = 1/42.
Together, (1/63 + 1/42) = 5/126 of work per hour.
Total time = 126/5 hours = 25.2 hours.
Working 8.25 hours per day, they will finish in 25.2 ÷ 8.25 = 3 days.

If A and B together can complete a piece of work in 15 days and B alone in 20 days, in how many days can A alone complete the work?
a) 60
b) 45
c) 40
d) 30

a) 60
Explanation: (A + B) can complete the work in 15 days, so one day’s work = 1/15.
B alone can complete the work in 20 days, so one day’s work = 1/20.
Therefore, A’s one day’s work = 1/15 − 1/20 = 1/60.
Hence, A alone can complete the work in 60 days.

Ajit has a certain average for 9 innings. In the tenth innings, he scores 100 runs thereby increasing his average by 8 runs. His new average is:
a) 20
b) 21
c) 28
d) 32

c) 28
Explanation:
Let Ajit's average for 9 innings = \(x\).
Total runs in 9 innings = \(9x\).

In the 10th inning, he scores 100 runs.
New average = \(x + 8\).
Total runs in 10 innings = \((x + 8) \times 10\).

Equation:
\[ 9x + 100 = 10(x + 8) \]
\[ 9x + 100 = 10x + 80 \]
\[ x = 20 \]
New average = \(x + 8 = 28\).