Ratios and Proportions


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Ratios are used to compare quantities. To compare two quantities, the units of the quantities must be the same. Ratios help us to compare quantities and determine the relation between them. We write ratios in the form of fractions and then compare them by converting them to like fractions. If these like fractions are equal, then the ratios are said to be equivalent.

e.g. Cost of 6 pens is Rs 90. What would be the cost of 10 such pens? 
Solution: Cost of 6 pens = Rs 90
              Cost of 1 pen = 90 ÷ 6 = Rs 15
              Hence, cost of 10 pens = 10 × 15 = Rs 150.

When two ratios are equivalent, the four quantities are said to be in proportion.

Ratio and proportion problems can be solved by using two methods, the unitary method and equating the ratios to make proportions, and then solving the equation.

Unitary method
Unitary method is the method of finding the value of one unit (unit rate) at first and then the value of required number of units.

Percentage is another method used to compare quantities. Percent is derived from the Latin word ‘per centum’, which means per hundred. Percentage is the numerator, of a fraction, whose denominator is hundred. Percent is represented by the symbol - %.
e.g. 21 100 or 21%

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1 . A Sells a bicycle to B at a profit of 20% and B sells it to C at a profit of 25%

S.P = 1500;B profit%=25 %
=> C.P for B = 100 *1500 = 1200
=> C.P for B = S.P for A...

2 . The monthly salary of a typist is Rs.15625

Given monthly salary of a typist = Rs 15,625
Percentage increase in salary = 12%
Hence 12% of Rs 15,625 = (12/100) × 15625...

3 . The ages of two persons are in the ratio 5:7

Age of two persons 18 years ago are (5x â 18) and (7x â 18) years Given (5x â 18)/(7x â 18) = 8/13 13(5x â 18) = 8(7x â 18) 65x...

4 . cost of an item is rs50 . it was sold with a profit of 12% .

12% profit on Rs 50 = 12/100 X 50 = Rs 6 Sp = cp+ profit = 50+6=Rs 56 so the selling price is Rs56

5 . What is the percentage of students who play both the games?

Let the number of students in the school be 100.
Numer of students who play football = 40% of 100 = 40
Numer of...