# 100 SHORTCUTS to crack QUANTITATIVE APTITUDE

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Ratio and Proportion
Partnership
Mixtures and Allegation
Average
Percentage
Profit, Loss and Discount
Problems on Ages
Time, Speed and Distance
Trains
Boats
Time and Work
Pipes and Cisterns
Simple and Compound Interest
Number System
HCF and LCM
Heights and Distances
Progressions
Calendar
Clocks
Permutation and Combination
Probability

### Ratio and Proportion

Question:

Container 1 has milk and water in the ratio 2: 5. After adding 4 liters of pure water from container 2, the ratio between milk and water in container 1 became 1 : 3. Find the quantity of milk in the container.

Let us assume the actual quantity of milk and water as 2x and 5x.
New quantity of water = 5x + 4
2x/(5x+4)= 1/3
6x=5x+4
x=4
Quantity of milk = 2x
= 2(4)
= 8 liters.

#### Question 1:

Average age of 5 students was 18. After adding teacher’s age the average became 20. What is the age of the teacher?

Answer = (18 x 5)~ (20 x 6) = 30

Question 2:

Average age of 5 students and a teacher was 21. After removing the teacher’s age the average became 18. What is the age of the teacher?

Answer = (21 x6) ~ (18 x 5) = 36

Question 3:

Average weight of 40 bags is 20kg. After removing 1 bag the average became 19.5. What is the weight of removed bag?

Answer = (20 x 40)~ (19.5 x 39) = 39.5

Question 4:

Average weight of 40 bags is 20kg. After replacing a bag by another bag the average became 39. What is the difference between the weights of those two bags?

Answer = (20 x 40)~ (20 x 39)=20

### Time and WorkTime is inversely proportional to Resource

T1        R2
—— = ——

T2        R1

Question:

If 20 men can do the work in 40 days, how many men are required  to do the same work in 10 days?

R1 = 20; R2 =?

T1 = 40; T2 = 10

Substitute the values in the above formula, we get

20/R2 = 10/40

R12 = 80

### Three resources working together

ABC                     1          1            1            1
T= —————–  or  —— = ——- + —— + ———
AB + BC + AC            T            A           B             C

Question:
A can do a work in 40 days, B in 50 days and C in 60 days. If they  work together, how long will they take to complete the work?

A = 40

B = 50

C=60

Substitute the values in the above formula, we get Time taken

together = (40 x 50 x 60)/(40+ 50+60) = 16.21 days