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**Quantitative Aptitude Study Notes for Bank Exams PO and Clerk**

**RATIO AND PROPORTION SHORTCUT TRICKS**

You know that quantitative
aptitude portion is most important in

**bank PO and****Clerk Exams**and for other competitive exams because if you want a good score in bank exam then you have to score good in maths.**Ratio and proportion shortcut tricks**questions are very important questions for quantitative aptitude section in**Bank Exams**for SBI, IBPS, RRB PO and CLERK exams and other competitive exams. In competitive exams the most important thing is time management, if you know how to manage your time then you can do well in**Bank Exams**. That’s where Maths shortcut tricks and formula are comes into action. Examples on All shortcut tricks on**RATIO AND PROPORTION for bank exams**are provided below in this page. These examples will help you to better understand**shortcut tricks on ratio and****proportion.****RATIO:**

The number of times one quantity
contains another quantity of the same kind is called the ratio of the two
quantities or Ratio is a quantity which represents the relationship between two
similar quantities.

For example the ratio 4 to 5 is
written as 4:5 or 4/5. 4 and 5 are called the terms of the ratio. 4 is the
first term and 5 is the second term.

Here first term or numerator i.e.
4 is called the ANTECEDENT and second term or denominator i.e. 5 is called the
CONSEQUENT.

**PROPORTION:**

Consider the two ratios:

1

^{st}Ratio 4:12
2

^{nd}Ratio 7:21
From the first ratio 4 is the
one-third of 12, and form the second ratio 7 is the one-third of 21. By this
both the ratios are equal. So the equality of ratios is called PROPORTION.

The 4, 12, 7 and 21 are said to
be in proportion.

The proportion may be written as

4 : 12 : : 7 : 21

Or

4:12=7:21

Or

4/12=7/21

The numbers 4, 12, 7 and 21 are
called the terms, 4 is the first term, 12 is the second term, 7 is the third
term and 21 is the fourth term.

First and fourth terms are called
the extremes terms, and the second and third terms are called as mean terms.

**Examples with shortcut tricks on ratio and proportion are given below:**

Ex for compound ratio: Find the
ration compounded of the four ratios:

2:3, 4:5, 8:21, 7:10

Solution: the required ratio = 2×4×8×7/3×5×21×10;
32/225

Inverse ratio:

If 9:7 be the given ration, then
1/9:1/7 or 7:9 is called its inverse or reciprocal ratio.

**Ex: divide 1562 into two parts such that one may be to the other as 5:6.**

**Solution:**

1

^{st}part = 5×1562/5+6
=5×1562/11

=700

2

^{nd}part = 6×1562/11
= 852.

**Ex: A, B, C and D are four quantities of the same kind such that**

**A:B=3:4, B:C=8:9, C:D=15:16**

a)
Find the ratio A:D

b)
Find A:B:C

**Solution:**

a)
A/B=3:4, B/C=8:9, C/D=15:16

Then; A/D= A/B × B/C × C/D

= 3/4 × 8/9 × 15/16

= 7:30

b)
A:B=3:4 = 3*2:4*2; Now A:B becomes 6:8, the value of B becomes
equal in both the ratios, in ratio A:B and B:C i.e. 6.

By this the ratio A:B:C will be
6:8:9

**Ex: the ratio of the money with Anu and Sheetal is 7:15 and that with Sheetal and Poonam is 7:16. If Anu has 490 Rs. Then how much money does Poonam have?**

**Solution:**Anu:Sheetal:Poonam;

7 : 15

7 :
16

49: 105 : 240

The ratio of money with
Anu:Sheetal:Poonam is 49: 105 :
240

So Poonam have Rs. 2400.

**Ex: one man adds 3 litres of water to 12 liters of milk and another 4 liters of water to 10 liters of milk. What is the ratio of the strengths of milk in the two mixtures?**

**Solution:**Strength of milk in the first mixture = 12/12+3=12/15

Strength of milk in the second
mixture = 10/10+4 = 10/14

Then the ratio of strengths =
12/15 : 10/14

=12*14 : 15*10 = 28:25

**Ex: find the fourth proportional to the numbers 7, 21 and 3.**

**Solution:**if x be the fourth proportional, then 7:21=3:x

X=21×3 / 7;

= 9

**Ex: if 8 men can reap 80 hectares in 24 days, how many hectares can 36 men reap in 30 days?**

**Solution:**1

^{st}: if 8 men can reap 80 hectares, then 36 men reap in

8 M : 36 M = 80 hectares : x no
of hectares

X = 36×80 / 8 =360 hectares

2

^{nd}: if 360 hectares can be reaped in 24 days, then hectares reaped in 30 days is
24 days : 30 days = 360 hectares
: x no. of hectares

X= 30×360 / 24

= 450.

**Ex: divide Rs 1350 into three shares proportional to the numbers 2, 3 and 4.**

**Solution:**1

^{st}share = Rs 1350 × 2 /2+3+4

= 1350 × 2/9; = Rs 300

2

^{nd}share = Rs 1350×3/9 = Rs 450
3

^{rd}share = Rs 1350 × 4/9 =Rs 600

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