Posted by: Kunal | February 5, 2008

Daily Dose

Todays dose  will be on Maths.

Lets start from the basics, and discuss what Ratios are all about.

Let the two quantities be X and Y. Both of them have same units. Then, the ratio is defined as the fraction that one quantity is relative to the other.

Ratio = X/Y = X : Y

Now, let us take an example to get an overview of the problems.

Example: Divide Rs. 1,500 in between Ram and Rahim in the ratio of 7:8. Find the individual share of them.

Solution. The following are the steps to get with these type of questions

Sum of the ratio = 7 + 8 = 15

Ram’s share = 7/(7 +8) × 1500 = 7/15 × 1500 = Rs. 700

Similarly, Rahim’s share = 8/(7+8) × 100 = 8/15 × 1500 = Rs. 800

This is the basic concept that is applied to all questions under this category. The difficulty level may vary from question to question because certain other concept are mixed with it.

Let us have an example

Example: If A : B = 3 : 2 and B : C = 3 : 4, then find the value of A : C.

(This question will answer your query pertaining to the question asked and another common question What is the value of A: B : C)

Solution. A : B = 3 : 2 and B : C = 3 : 4.

Step-I. Identify the non-essential term(s). Here, it is B. (We have to find the ratio between A and C)

Step-II. Check out whether the fractional parts of B in the given two quantities are equal? Here, they aren’t equal because with A it’s 3 and with C it’s 2.

Step-III. If the value of the non-essential term is not equal then we have to equate it. This can be done by multiplying it with any positive integer (minimum) such that both of the fractional parts become equal.

A : B = (3 : 2) × 3 = 9 : 6

and B : C = (3 : 4) × 2 = 6 : 8

Now, we can see that the fractional part of B is equal in both of the given ratios. Hence, we can conclude that A : C = 9 : 8.

What is the value of A: B : C??

Solution. In such type of questions, we have to equate any one of the given quantities. (As in the above part we have equated B) Now, all the three quantities are mutually related with each other. Hence, we can choose any two of them and their respective ratios.

OR

A/C = A/B × B/C = 3/2 × ¾ = 9 : 8

From this method we can answer only to the question asked.

Try this one of your own!!

Question. Two types of tea are mixed in the ratio of 3 : 5 to produce the first quality and if they are mixed in the of ratio of 2 : 3, the second quality is obtained. How many kilograms of the first quality has to be mixed with 10kg of the second quality so that a third quality having the two varieties in the ratio of 7 : 11 may be produced? (NALSAR 2007)


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Responses

  1. Is the answer 7.5kg?

  2. Is the answer 8kg?

  3. heylo!!
    whats the answer to the question??is the solution going to be posted??

  4. i think the answer is 8 kg

    my soln
    frm 10 kg of 2nd quality we have 4 kg of 1st variety nd 6 kgs of 2nd variety as the ratio is 2:3……..let us assume that frm the first quality we have 3x kg of 1st variety nd 5x kg of 2nd variety as the ratio is 3:5…..
    As given that the final quality has the two types of tea in the ratio 7:11…….therefore: (4+3x)/(6+5x)=7/11……..solving we get x as 1…….hence total amnt of 1st quality tea is (3*1+5*1=)8kg


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