Quantitative Aptitude – Time, Work and Distance

Quantitative Aptitude or commonly called as the mathematical section of Aptitude is a crucial part in getting placement in many companies that prefer quantative ability evaluation. Many big companies like Infosys, TCS and many others have their first round an Aptitude Test.

To correctly crack the test in time, it’s important to learn to understand how the solution to a particular type of situation or question is reached. There are many easy, shorthand tricks and various formulas for easy understanding and quick answering of the questions under this section.

There are many topics that come under quantitative aptitude like,

  1. Time and Work
  2. Probability
  3. Boats and Streams
  4. Permutation and Combination
  5. Simple and Compound Interest
  6. Heights and Distances, etc.

Here we will discuss how to solve questions based on relation between Time and Work.

Note:



  1. If X is two times better than Y in completing the work then:
    Time taken by X to finish work : Time taken by Y to finish work = 1:3
    Work done by A : Work done by B = 3:1
    Here, ” : ” denotes ratio.

  2. How to find no. of days taken to complete given amount of work:
    If X’s 1 day’s work = 1/m then it will take X, m days to finish given work.

  3. How to find amount of work done from given number of days:
    If X can do some work in m days, then work done by X in one day = 1/m

Que-1:
A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in?

Explanation:
Let B take x days to complete the work alone.
So,

1/x + 1/12 = 1/8 
=> 1/x = 1/8 – 1/12 = 1/24 
=> x = 24 

Que-2:
If 3 men or 4 women can construct a wall in 43 days, then the number of days that 7 men and 5 women take to construct it is?

Explanation :

3 men = 4 women or 1 man = 4/3 women 

Therefore,

7 men + 5 women = (7 × 4/3 + 5) women 

i.e., 43/3 women
4 women can construct the wall in 43 days
Therefore, 43/3 women can construct it in = 12 days



Que-3:
Arnold alone can do some work in 6 days and Brat alone can do the same work in 8 days. Arnold and Brat decided to do it for $3200. With the help of Carl, they completed the work in 3 days. How much is to be paid to Carl?

Explanation :
Carl’s 1 day’s work

= 1/3 – (1/6 + 1/8) = 1/3 – 7/24 = 1/24 

Arnold’s wages : Brat’s wages : Carl’s wages can be written as ->

1/6 : 1/8 : 1/24 = 4:3:1 

So, Carl’s share,

= 1/8 * 3200 = $400  

Que-4:
A tank has four inlet pipes.When first three inlet pipes are opened together, tank can be filled in 12 min and when the last three inlet pipes are opened together, tank can be filled in 15 minutes and by the first and last inlets only, tank can be filled in 24 minutes. What is the time taken by last pipe to fill half of the tank?

Explanation :
Let the four inlet pipes be P, Q, R and S respectively.
Given,

P + Q + R together can fill the tank in = 12 min 
Q + R + S together can fill the tank in = 15 min 
P + S together can fill the tank in = 24 min 

So, Total capacity of the tank = 120 units (L.C.M of time taken by all 4 inlet pipes be P, Q, R, and S).

Now, Efficiency of inlet pipes P + Q + R = Total capacity of the tank/ Time taken by P + Q + R together to fill the tank

= 120/12 = 10 units/minute 

Similarly, Efficiency of inlet pipes Q + R + S = 120/15 = 8 units/minute
and Efficiency of inlet pipes P + S = 120/24 = 5 units/minute

On Adding all the obtained efficiencies, we get,



2(P + Q + R + S) = 23 units/minute 

Efficiency of (P + Q + R + S) = (23/2) units/minute
Efficiency of S,

= (23/2) – Efficiency of (P + Q + R) 
= (23/2) – 10 
= 3/2 units/minute 

Time taken by last pipe (S) to fill half of the tank

= (1/2) * [Total capacity of the tank/Efficiency of pipe S] 
= (1/2) * [120/(3/2)] 
= (1/2) * [(120 * 2)/3] 
= 40 mins 

Que-5:
Either 6 women or 17 men can paint a wall in 33 days. The number of days required to paint three such walls by 12 women and 32 men working at same rate?

Explanation :

6 women = 17 men 
1 women = 17/6 men 
Total work = 17*33 

One day efficiency of 12 women and 32 men

= 12 women + 32 men 
= (12*17)/6 men + 32 men 
= 34 men + 32 men 
= 66 men 

Days required for 12 women and 32 men

= (17*33)/66 = 8.5 days 

The number of days required to paint three such walls

= 8.5*3 = 25.5 days 

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