Numerical Ability

1.  At the start of business A invested some money. After 4 months B joined by investing twice amount as A and after 8 months from start of business C invested thrice amount as A invested. If the total shares of A and C is Rs 30,000, what is the total profit received at the end of year?

Explanation:
Let A invested x for 12 months, then B for 2*x = 2x for (12-4) = 8 months, and C invested 3*x = 3x for (12-8) = 4 months. So A : B : C =
x*12 : 2x*8 : 3x*4
3 : 4 : 3
So (A+C) gets [(3+3)/(3+4+3)] * y = 30,000
Solve y = Rs 50,000

A mixture contains milk and water in the ratio 7 : 2. 9 litres of this mixture is taken out and 5 litres of water is poured in. If the ratio of milk to water becomes 14 : 5, what is the amount of milk originally present in the mixture?

 Explanation:
Total = 7x+2x+24 = 9x+9
So 7x/(2x+5) = 14/5
Solve, x = 10
So total = 9*10 + 9 = 99 litres
So milk = 7/(7+2) * 99 = 77

The ratio of monthly salaries of son to father is 2 : 5, and that of mother to son is 3 : 2. If son’s annual salary is Rs 3,00,000, then what is the monthly salary of mother?

Explanation:
S : F = 2 : 5, M : S = 3 : 2
Or F/S = 5/2, and S/M = 2/3, So F : S : M = 5*2 : 2*2 : 2*3 = 10 : 4 : 6 = 5 : 2 : 3
Annual salry of son = 3,00,000 so monthly is 3,00,000/12 = 25,000
So 2/(5+2+3) * x = 25,000
Solve, x = 1,25,000
So mother’s monthly salary = 3/(5+2+3) * 1,25,000 = 37,500

Tarun and Varun alone can do a piece of work in 20 and 25 days respectively. In how many days the work will be completed if they both work on alternate days starting with Varun?

Explanation:
Tarun = 20 days, Varun = 25 days
Total work =1/20+1/25=9/100

[here is a small technique, Total work done will be 1, right, then multiply numerator till denominator, as 9*11 =99, 9*12 = 108, as  9*12  is more than 100, so we will consider 9*11, means 11  pairs ]

2*11(22) days work of both = 9*11 = 99
So remaining work = 100-99 = 1
Now Varun’s turn on 23rd day, he will do remaining work(1) in 1/4 day (25*4)
So total 22 1/4 days

How many 4 digit numbers can be made from the digits 2, 3, 5, 0, and 9 without repetition?

Explanation:
0 cannot be on first place for it to be a 4 digit number,
So for 1st digit 4choices, for second also 4 (because 0 can be placed here), then 3 for third place, 2 for fourth place
Total numbers = 4*4*3*2

476, 480, 479, 495, 490, 522, 497  

Explanation:
476 + 2^2, 480 – 1^2, 479 + 4^2, 495 – 3^2, 486 + 6^2, 522 – 5^2, 497

SO, Here Ans come 490

11, 18, 35, 80, 159, 286

Explanation:
18 – 11 = 7, 37 – 18 = 19, 80 – 37 = 43, 159 – 80 = 79, 286 – 159 = 127
19 – 7 = 12, 43 – 19 = 24, 79 – 43 = 36, 127 – 79 = 48  (Double Series)

SO, Here Ans come 35

112, 224, 280, 308, 322, 330

Explanation:
112+(112/1), 224+(112/2), 280+(112/4), 308+(112/8), 322+(112/16), 329

SO, Here Ans come 330

444, 440, 431, 420, 390, 354

Explanation:
444 – 2^2, 440 – 3^2, 431 – 4^2, 415 – 5^2, 390 – 6^2, 354

SO, Here Ans come 420

24, 12, 18, 45, 157.25, 708.75

Explanation:
24*0.5, 12*1.5, 18*2.5, 45*3.5, 157.5*4.5, 708.75

SO, Here Ans come 157.25

Study the given line graph carefully and answer the questions that follow.
The graph given below shows the number of employees in two departments of company ABC from year 2010 to 2015.

In which year is the percentage increase in the number of employees over the previous year the highest for IT department?

Explanation:
In 2011, % increase is (2600-1800)/1800 * 100 = 44.4%
In 2012, 2013 the number is decreasing
In 2014, % increase is (2050-1950)/1950 * 100 = 5.12%
In 2015, % increase is (2200-2050)/2050 * 100 = 7.3%

Number of employees in HR department is approximately what percentage of the total number of employees in both departments together in the year 2014?

Explanation:
In 2014, in HR = 1200
In HR + IT = 1200 + 2050 = 3250
So required % = (1200/3250)*100 = 36.9

What is the average number of employees in IT Department over all years?

Explanation:
1800+2600+2400+1950+2050+2200 / 6 = 2166

Number of employees in HR department in 2012 is what percent less than that of IT department in the same year?

Explanation:
(2400-1900)/2400] * 100 = 20.8%

What is the difference between the averages of number of employees in both departments for all the years?

Explanation:
Average in IT department = 1800+2600+2400+1950+2050+2200 / 6 = 2166
Average in HR department = 1400+2700+1900+2100+1200+1500 / 6 = 1800
Difference = 2166-1800 = 366