UNIT Ratio F.Y.B.COM Prof.P.A.Navale Dept. of Commerce

Introduction The topics, ratios, proportion and percentages are concerned with dividing something into parts. A ratio shows the relative sizes of two or more values. Ratios can be shown in different ways. Using the ":" to separate. A ratio is one thing compared to or related to another thing; it is just a statement or an expression. A proportion is two ratios that have been set equal to each other; a proportion is an equation that can be solved. A percentage is a fraction whose denominator (bottom) is 100. So if we say 50%, we mean 50/100 = 1/2 (after cancelling). So 50% means ½. If want to find 10% of something, 'of' just means 'times'.

Ratio Meaning: A ratio is a comparison of the relative values of numbers or quantities. We can write a ratio for any statement containing such a comparison. For example, that there are twice as many married employees as single employees, we mean that the ratio of married to single employees is 2:1, where 2 represents married employees and 1 represents single employees.   Definitions: Giri & Banerjee: “A ratio a: b is said to be the ratio of greater inequality if a > b and of lesser inequality if a < b. lf a = b, the ratio a : b is called the ratio of equality.” b) Om P. Chug: “A ratio is a comparative relationship of two similar quantities with regards to their magnitudes and expresses what multiple or pan the first quantity is of the second.”

Ratio Example: The ratio of the no. of boys to the no. of girls in a school of 720 students is 3: 5. If 18 new girls are admitted in the school, find how many new boys may be admitted so that the ratio of the no. of boys to the no. of girls may change to 2: 3. Solution: The ratio of the no. of boys to the no. of girls = 3:5 Sum of the ratios = 3 + 5 = 8 So, the no. of boys in the school = (3 x 720)/8 = 270 And the no. of girls in the school = (5 x 720)/8 = 450 Let the no. of new boys admitted be x, then the no. of boys become (270 + x). After admitting 18 new girls, the no. of girls become 450 + 18 = 468 According to given description of the problem, (270 + x)/468 = 2/3 or,3(270+x)=2x468 or, 810 + 3x = 936 or, 3x = 126 or, x = 42. Hence the no. of new boys admitted = 42.

Ratio Types of Ratio: Types of Ratio Continued Ratio Inverse Ratio

Ratio Continued Ratio: Continued Ratio is the relation (or comparison) between the magnitudes of the same kind. The continued ratio of three similar quantities a, b, c is written as a:b: Example: Suppose that Rs. 74000 are to be divided among three friends A, B, C such that A : B = 4 : 5 and B : C = 3 : 2 Sum of ratio = 12 15 10 = 37 Share of A = Share of B = Share of C =

Ratio 2) Inverse Ratio: One ratio is inverse of another if their product is 1. Thus a:b is the inverse ratio of b/a and vice versa. Example:  The monthly incomes of two persons are in the ratio 4: 5 and their monthly expenditures are in the ratio 7: 9. If each saves Rs. 50 per month, find their monthly incomes. Solution: Let the monthly incomes of two persons be Rs. 4x and Rs. 5x so that the ratio is Rs. 4x: Rs. 5x = 4: 5. If each saves Rs. 50 per month, then the expenditures of two persons are Rs. (4x - 50) and Rs. (5x - 50). Hence, the monthly incomes of the two persons are Rs. 4 x 100 and Rs. 5 x 100 i.e. Rs. 400 and Rs. 500.

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