**Percentage**

##### 1…..

Try to convert percentage into fraction:-Some important are given below

50%=1/2 | 16.66%= 1/6 |

66.66%= 2/3 | 25%= ¼ |

75%= 3/4 | 20%= 1/5 |

40%= 2/5 | 60%= 3/5 |

33.33%=1/3 | 83.33%= 5/6 |

##### 2**……**

**Condition 1 ^{st}** :- If

**a**is increased by

**p%**then we have to decrease it by (p/(p+100)×100)% to get the value

**E.G** if kamal has 33.33% more pencil than shyam then by how much shyam has less pencil than kamal

**Sloution : **33.33%= 1/3, kamal>shyam by 1/3 so shyam<kamal by 1/1+3= ¼ = 25%

**Condition 2 ^{nd}**:- if kamal has 25% less pencil than shyam then by how much shyam has more pencil than kamal.

**Solution:–** 25%= ¼, kamal<shyam by 1/4 so shyam>kamal by 1/4-1=1/3= 33.33%

##### 3……

Q: If a is greater than b by 25% then find the value of b

Solution: Generally students do: b×25%=b/4, then

b+b/4=a

5b/4=a

b=4a/5

But shortcut is b is 1/(1+4) less than a

so b is 1/5 means 20% less than a

means 80% of a= b

4a/5=b

##### 4…..

**Q:** if we have to calculate 21% of 2547

simply do following steps

(20+1)% means first find 20% & then 1% (it makes solution very easy)

20% of 2547= 509.4…………i

1% of 2547= 25.47……………..ii

Now i+ii = 534.87

same thing can be done with 29=30-1 etc…

**RATIO AND PROPORTION**

##### 1…..

**Q:** If A:B=1:2,B:C=2:5,C:D=2:3 AND D:E=1:3, FIND A:E.

**Solution:** A:B=1:2

B:C=2:5

C:D=2:3

D:E=1:3

A:B:C:D:E=1×2×2×1 **: **2×2×2×1 **: **2×5×2×1 **: **2×5×3×1 **: **2×5×3×3 (see the pattern)

So, A:E=1×2×2×1:2×5×3×3 =4:90

##### 2….

*Partnership problem can easily solved by ratio*

**E.G:- **P started some business with Rs.6000. After 3months B joined him with 2000 and after some more time R joined them with 5000.At the end of the year total profit of 2500, R gets 1500. After how many R join w.r.t to P

**Solution:** Share of P:Q:R=6000×12:2000×10:5000×x=72:2:5x (multiplying share with working months)

So, 5x:74+5X=500:2500

5x:74+5X=1:5

25x=(74)+5x

20x=74

X=3.75

Means R joins after 8 months(approx.)

**Note:- you can also try Age problems on this basis. **

** DI (DATA INTERPRETATION)**

Well, this is the most important section throughout the aptitude section

For DI you need to practice

- Division rule
- Percentage
- Ratio

Percentage and Ratio is already discussed so next one is Division tricks.

**1…..**

**Q:-** If 782/985

**Solution:- **Step 1:- Let 782 be 800 and 985 be 1000

So, 800/1000= 0.8

Step 2:– 985 is 15 less than 1000(**always take denominator**)

Step 3:-so multiply 15 to 0.8= 15*0.8= 12

Step 4:– add 12 to 782=782+12=794

Step 5:- divide 794 to 1000=794/1000= 0.794

If percentage is asked then it will be 79.4

You can do it with another eample

**Q:-** If 416/816

**Solution:- **Step 1:– Let 416 be 500 and 816 to 900

Step 2:– 500/900= 0.5

Step 3:- 816 is 84 less than 900 so 84*0.5= 42

Step 4:– 416+42=458

Step 5:- 458/900=0.508

So in percentage 50.8% (approx)