RATIO

Ratio – Ratio can be defined as the mathematical relation or comparison between two or more unequal quantities. It is represented by the symbol “: “.E.g. – If A’s age is 10 yrs and B’s age is 13 yrs thenThe ratio between A’s and B’s age is 10:13.Here first quantity is known as Antecedent and second quantity is called consequent. Type of ratio:-

(a) Inverse or reciprocal ratio :- In this type of ratio, if the antecedent increases then the consequent decreases and if the antecedent decreases then consequent increases.

E.g. – Inverse ration of above example is 1/10:1/13 = 13:10 It means that this ratio can be obtained by interchanging the antecedent and the consequent of the given ratio. (b) Compound ratio – It is the ratio between the product of antecedent and consequent of two or more quantities. E.g. – The compound ratio of (4:5), (5:7), and (7:9) = (4*5*7): (5*7*9) Note:- It means that if we compound a ratio with itself, it becomes a duplicate ratio.  (c) Duplicate ratio – It is the ratio of the square of the original quantity. E.g. – Duplicate ratio of the ratio 4:5 is 16:25. (d) Sub duplicate ratio – It is the ratio of the square root of the original quantity. E.g. – Sub duplicate ratio of the ratio 16:25 is 4:5. (e) Triplicate ratio – It is the ratio of the cube of the original quantity.E.g. – Triplicate ratio of the ratio 4:5 is 64:125

PROPORTION

Proportion:- It is a statement which says that quantities are in proportion, if the ratio of the first two quantities is equal to the ratio of the last two quantities.

E.g. – let us have four quantities a, b, c and d. they will be said to be in proportion, if a/b = c/d or a: b = c: d Note – In the proportion quantities are on the outside is known as the extremes and the quantities on the inside is known as the means. Types:- (a) Direct proportion – Quantities are said to be in direct proportion; if one quantity is increased then other quantity is also increased. E.g. – The quantity x and y will be said to be in direct proportion if x = Ky or x/y = K where K is the constant of proportion. (b) Indirect proportion – Quantities are said to be in indirect proportion if one quantity is increased then other one is decreased. E.g. – The quantity x and y will be said to be indirect proportion if x = K 1/y where k is the constant of proportion. (c) Continued proportion – It is also called relational proportion. In this case ratio of the first quantity to the second quantity is equal to the ratio of the second quantity to the third quantity. It means that if x:y = y:z, then x, y, and z are said to be in continued proportion

Tricks Part I

Trick 1. If the ratio between the 1st  and 2nd  quantities is X : Y and the ratio between 2nd and 3rd quantities is P : Q, then the ratio among all these entities

1st : 2nd : 3rd = XP : YP : YQ Q1. The ratio of the age of Neera and Pummi is 7 : 4 and Pummi and Juli is 5 : 3. If the age of Juli is 16 yrs, what is the age of Neera?

 Ans:-N : P = 7 : 4 and P : J = 5 : 3 So, N : P : J = 35 : 20 : 12Here, 12 = 16 then 35 = 46.6 yrs (approx)  Trick 2. When four quantities P, Q, R and S are in proportion, there will be P × S = Q × R Note :- please note that the above trick is not only a trick but a basic theory of almost all question of time, works and wages chapter. Let us see few questions:- Q2. If 25 kms is covered in 5 hrs by a bike, then how much time will be taken to cover 55 Kms by the same bike? Ans:- I know all of you will answer like a bullet. But, let us solve this using trick no.2.25 : 55 ∷ 5 : ? So, ? = (55 × 5)/25 = 11 hrs. (It is so simple, just write Ratio of same factor = Ratio of corresponding factors) Q3. If 25 people complete a work in 8 days, then how much days will be taken by 10 people to complete the same work? Ans:- Close your eye and write 25 : 10 ∷ 8 : ?So, ? = (10 × 8)/25 = 80/25 = 3.2 daysOh, what a funny answer! We must be working with Reliance Industries as HRD manager. Less people = more workSo, have you understood? Just judge the corresponding Ratio of the factors.Here, 10 : 25 ∷ 8 : ? (Because less men, more time, less output)So, 10 × ? = 25 × 8 →  ? = 20 days Q4. If 6 persons can dig a well up to 36 Mtrs in 10 days, how much depth can 12 persons dig in 20 days? (This question can be solved with common sense, do not try it) Ans:- (6 persons : 12 persons ∷ 20 days : 10 days) ∷ 36 Mtrs : ?So, 60 : 240 ∷ 36 : ? → ? = 144 Mtrs 

Have you understood?Let me become informal. (If more = more, you were writing just corresponding. But, if more = less, you have to write just opposite) Q5. If 14 persons can finish a piece of work in 24 days putting 08 hrs a day, then in many days will 24 persons working 14 hrs a day to finish the same amount of work? (Do not try your common sense, just use the trick) Ans:- (14 P : 24 P ∷ 14 H : 8 H) ∷ ? : 24 (Here two things used (i) More P = Less H and (ii) More P = Less D)So, ? = 8 days. Trick 3. If A : B = X : Y, B : C = P : Q and C : D = M : Nthen A : D = X × P × M = Y × Q × N

Tricks - II