Ratio & Proportion

Hello friends…

Today we are going to learn about Ratios & Proportion. Generally all kinds of problems or all other topics under QA has something to do with this chapter.

We can say, this is sole of QA. Even answer options are guessed by this chapter. If we talk about the scope of this chapter, then it is very large. But for banking it is reduces by some books. If you want to work with full scope of this chapter then online examples & their solution are good way to learn them.

In this chapter we are going to learn few basic things about this chapter & as usual some vital techniques regarding the ration & proportion.

Firstly, Ratios are of two types,

1.    One that is greater than 1 &

2.    other ones those are less than 1

Example, 2/5 is less than 1, & 5/2 is greater than 1.

Two quantities are in the ration if they form p/q, where q not equal to 0. Well, we all know that.

Usage of ratio, suppose two workers have efficiency as “If one complete a work in 1.5 days other complete in 2 days” so we write it as 1.5/2 = (3/2)/2 = ¾ & express in terms of ratio as 3:4. This can be read as “If one completes the work in 3 UNITS other takes 4 UNITS for same work”

Now suppose they both worked together & earn Rs. 7000 then their share must be 3 Parts to 4 Parts. So first will take Rs. 3000 & other will take Rs. 4000. 

Calculating Actual Quantities :

This 3:4 is ratio. There is pretty simple way for parting total quantity into such two parts, as we make parts of 7000 to 3000 & 4000.

It has 3 steps,

1.    Just add ratio & (3+4 = 7)

2.    then divide that full quantity by ratio’s addition(7000/7 = 1000)

3.    then take division & multiply with ratio(1000*3 = 3000 & 1000*4 = 4000)

This is mind trick by the way you won’t any paper & pencil for that.

I have another mind trick for Age relation examples.

 Just remember following things( for some examples)

1.    Age of any man never exceeds 80 or 120

2.    Most of the time only ratios are given so you can quickly count tables up to getting satisfactory answer or new ratio

3.    Sometimes, it is given that father is 4 times the age of son. In such a cases you can convert folds(X) into ratio as follows

Father = 4 X son

  Father         4

----------- = -------

   Son           1

Now you can count tables of 1 & 4 to satisfy expected parameters. Specially in case of Clerks & Talathi (Land Revenue Officer) same questions are asked.

Next, we will see some properties of ratios

suppose we have a/b ratio

then

a/b  = (a X anything)/ (b X anything but same as above anything)

next

if a/b = c/d then a+b/b = c+d/d, you can use this property for reducing or making numerator or denominator as you wish

Variations in this property are as follows,

let a/b = c/d then 

1.    a+b/a-b = c+d/ c-d --- योग वियोग क्रिया

2.    a-b/a+b = c-d/c+d ---- वियोग योग क्रिया

3.    a/a+b = c/c+d ---- योग क्रिया

4.    a/a-b = c/c-d ---- वियोग क्रिया

जब आप + करते है तो उसे योग कहा जाता है |  और जब आप – करते है तो उसे वियोग कहा जाता |

But on only one condition that no numerator or Dr becomes zero while making this adjustment

Also we know that calculating LCM & GCD of whole numbers is difficult than calculating GCD & LCM of ratios or fraction. That time you can use those properties.

Example application of above is as follows

suppose you want to find 12/5 but you cannot calculate it easily as this is too big no 12 to divide with 5

So what we do, we start adjusting it till we don’t get comfortable figures

so let 12/5 = x

then 12-5/5 = x-1/1

then 7/5 = x-1/1

then 7-5/5 = x-2/1

then 2/5 = x-2/1

Now we got comfortable figures  to calculate with so we calculate 2/5. As 2 parts of 5 is calculated as 1/5 X 2

Now we know 1 part of 5 is 20% = 0.2 so 2 parts will be 0.4

Now

0.4 = x-2/1

so x = 0.4 X 1 + 2 = 2.4

& that’s our answer for 12/5

This way you can find this योग वियोग application anywhere. Just stay focused on calculations.

Examples to Solve :
1) A and B together have Rs. 1210. If of A's amount is equal to of B's amount, how much amount does B have?

2) Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:

3) A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share? 


4) Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?

5 ) Find the fourth proportional to 2.4, 4.6 and 7.6?

A.) 14	B.) 14.657
C.) 15.56	D.) 14.56

6 ) Find the third proportional to 9 and 12?

A.) 9	B.) 108
C.) 16	D.) 9

7 ) Find the mean proportional between 49 & 81?

A.) 16	B.) 10
C.) 63	D.) 12

8) If Rs.800/- Rupees are divided among a,b and c in such a way that A’s share 4 times more than B, B’s share is 3 times more than C. The C’s share is?

A.) Rs.650/-	B.) Rs.600/-
C.) Rs.150/-	D.) Rs.50/-

9) If Rs.540/- are divided among A,B and C in such a way that A’s share is ½nd of B share and B’s share is 1/3rd of C’s share. The share of A is?

A.) Rs.80/-	B.) Rs.360/-
C.) Rs.60/-	D.) Rs.120/-

10) If Rs.1440/- are divided among A,B and C so that A receives 1/3rd as much as B and B receives 1/4th as much as C. The amount B received is:

A.) Rs.90/-	B.) Rs.270/-
C.) Rs.1080/-	D.) Rs.27/-

11) Rs.630/- distributed among A,B and C such that on decreasing their shares by RS.10,RS.5 and RS.15 respectively, The balance money would be divided among them in the ratio 3:4:5. Then, A’s share is:?

A.) Rs.150/-	B.) Rs.200/-
C.) Rs.160/-	D.) Rs.255/-

12)A bag contains 50p,Rs.1/- and Rs2/- coins in the ratio of 4:2:1 respectively. If the total money in the bag is Rs.60/-. Find the number of 50p coins in that bag?

A.) 60 coins	B.) 10 coins
C.) 20 coins	D.) 40 coins

13) Rs.4800/- are divided among P,Q and R in such a way that the share of P is 5/11 of the combined share of Q and R. The share of Q is 3/13 of the combined share of R and P. Thus, R gets:?

A.) Rs.300/-	B.) Rs.3300/-
C.) Rs.1500/-	D.) Rs.2400/-

14) Two vessels of equal volumes contains milk and water mixed in the ratio 1:2,2:3. When These mixtures are mixed to form a new mixture, what is the ratio of milk and water?

A.) 11:19	B.) 19:11
C.) 2:5	D.) None of these