Today our topic of discussion is Continued Ratio.
Continued Ratio
Continued Ratio
Let us assume that Roni’s earning is Tk 1000, Soni’s earning is Tk 1500 and Samir’s earning is Tk 2500. Here, Roni’s earning: Soni’s earning = 1000:1500=2: 3; Soni’s earning: Samir’s earning 1500:2500=3: 5. Hence, Roni’s: = Soni’s: Sami’s earning = 2:3 ; 5 .
If two ratios are of the form a : b and b : c they can be re-written in the form a: be. This is called continued ratio. Any two or more ratios can be expressed in this form. It is noted that if two ratios are to be expressed in the form a / b / c the antecedent of the first ratio and the subsequent of the second ratio need to be equal.
For example, if two ratios 2 : 3 and 4: 3 are to be put in the form a / b / c the subsequent quantity of the first ratio is to be made equal to the antecedent quantity of the second ratio. That is, those quantities are to be made equal to their L.C.M.
Here, L.C.M of 3 and 4 is 12.
Here, 2/3 = 2/3 = (2 * 4)/(3 * 4) = 8/12 = 8/12
Again, 4/3 = 4/3 = (4 * 3)/(3 * 3) = 12/9 = 12/9
Therefore, if the ratios 2 : 3 and 4:3 are expressed in the form, a: b: c will be 8:12:9
It is to be noted that if the earning of Sami in the above example is 1125, the ratio of their earnings will be 8: 12:9.
Example 12. If a, b, c are quantities of same kind and a :b=3:4, b : c = 6:7 , what will be a: b: c ?
Solution: a : b = 3/4 = (3 * 3)/(4 * 3) = 9/12 and b / c = 6/7 = (6 * 2)/(7 * 2) = 12 14 [LC.M. of 4 and
∴ a : b : c = 9:12:14
Example 13. The ratio of angles of a triangle is 3:45. Express the angles in degree.
Solution: Let the angles, according to given ratio, be 3, 4 and 5r. Sum of three angles = 108 °According to the problem, 3x + 4x + 5x = 180 °
or, 12x = 180 °
or, x = 15 °
Therefore, the angles are 3x = 3 * 15 °= 45 °
4x = 4 * 15 °= 60 °
and 5x = 5 * 15 °= 75 °
Example 14. If the sides of a square increase by 10%, how much will the area be increased in percentage?
Solution: Let, each side of the square be a metre. Therefore, the area of the square be a²square metre. If the side of the square increases by 10%, each side will be ( a + a of 10%) metre, or 1.10a metre. In this case, the area of the square will be (1.1a)² square metre, or 1.21a² square metre. Thus the the area increases by (1.21a² – a ²) = 0.21a² square metre.
∴ The percentage of increment of the area will be (0.21a²)/(a ²) * 100 %=21%
Work:
1) There are 35 male and 25 female students in your class. The ratio of rice and pulse given by each of the male and female students for making Khicuri in a picnic 3: 1 and 5/2 respectively. Find the ratio of total rice and total pulse.
2) The amount of pulse, mustard and paddy produced in a farmer’s farm are 75 kg, 100 kg and 525 kg, respectively. The grains are sold at price of 100, 120 and 30 taka respectively. After selling all the grains, calculate the ratio of income from the individual grain.
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