Quantitative Aptitude Study Notes for Bank Exams JKSSB and SSC
RATIO AND PROPORTION SHORTCUT TRICKS
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:
1st Ratio 4:12
2nd 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:
1st part = 5×1562/5+6
=5×1562/11
=700
2nd 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: 1st: 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
2nd: 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: 1st share = Rs 1350 × 2 /2+3+4
= 1350 × 2/9; = Rs 300
2nd share = Rs 1350×3/9 = Rs 450
3rd share = Rs 1350 × 4/9 =Rs 600
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