Ratio, Proportion & Unitary Method
Category : 6th Class
RATIO, PROPORTION AND UNITARY METHOD
RATIO
The comparison of two quantity of same kind by division is called ratio.
Example: Ratio between Rs. 30 and Rs. 50, but there can be no ratio between Rs. 30 and 50 apples, form of ratio \[=x:y\]
\[x\to \]antecedent
\[y\to \]consequent
Types of Ratio:
Example: \[a:b,\,\,c:d,\,\,e:f,\]then compound ratio is,\[\frac{a\times c\times e}{b\times d\times f}\]
Example: Find duplicate ratio of\[5:7.\]
Solution: \[{{\left( 5 \right)}^{2}}:{{\left( 7 \right)}^{2}}=25:49\]
Example: Find triplicate ratio of\[2:3\].
Solution: \[{{\left( 2 \right)}^{2}}:{{\left( 3 \right)}^{2}}=8:27\]
Solution: \[\sqrt{4}:\sqrt{9}\]
\[=\sqrt{2\times 2}:\sqrt{3\times 3}\]\[=2:3\]
Example: Find sub-triplicate ratio of\[1:8\].
Solution:\[\sqrt[3]{1}:\sqrt[3]{8}=1:2\]
Proportion;
\[w\times z=x\times y\]
\[wz=xy\]
Example: Let the four quantities 5, 10, 6 and 12 be in proportion.
\[\frac{5}{10}=\frac{6}{12}\]or \[5:10::6:12\]
Example: 9, 6 and 4 are in continued proportion for\[9:6::6:4\].
Hence, 6 is the mean proportional between 9 and 4, and 4 is called third proportional to 9 and 6.
Mean Proportion
Example: Find the fourth prepositional to the number 6, 8 and 15.
Let \[x\] be fourth proportional
\[\therefore \]\[6:8::15:x\]
\[6x=8\times 15\]
\[x=\frac{120}{6}=20\]
Unitary Methods
Example: If the cost of 4 pencils is Rs. 24. What will be the cost 7 pencils.
Solution: We have,
Cost of 4 pencils = Rs. 24
\[\therefore \] Cost of 1 pencil\[=Rs.\frac{24}{4}\]
\[=Rs.\left( \frac{24}{4}\times 7 \right)=Rs.\left( 6\times 7 \right)=Rs.42\]
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