**Prologue: A ratio is a collation of two similar quantities prevailed by dividing one quantity by the other.**

**For example the ratio between 3 and 6 will be 1:2 whereas a proportion is a name we give to a statement that two ratios are equal. For example a:b=c:d.**

(1) : The incomes of A and B are in the ratio 3:2 and their expenditures are in the ratio 5:3, if each saves Rs 2000, what are their expenditures?

A. Rs 3500, Rs 1400

B. Rs 5000, Rs 1200

C. Rs 2400,Rs 1300

**D. None of these**

**Solution:**In order to solve this sum we need to go through the options in order to derive the correct answer Here we are been asked to find their expenditures so we need to get the ratio of amounts as given in the options similar to the ratio of expenditure stated in the problem , so starting with option A we find that 3500:1400=5:2 but as stated in the problem the ratio must be 5:3, hence option A is not correct .Checking with the rest of the options we find that our correct option is D.

(2) : A sum of Rs 53 is divided among A,B and C in such a way that A gets Rs7 more than what B gets and B gets Rs 8 more than what C gets ,find the ratio of shares?

**A. 25:18:10**

B. 15:20:18

C. 51:11:12

D. 24:33:11

**Solution:**Now lets us take a challenge to solve this sum in a short cut method rather than using long and traditional methods. The question says a total sum of Rs 53 needs to get divided among A,B and C so first by looking at the options we should first try to find out which ratio adds up to Rs 53 so starting with option A we find that 25:18:10 i.e 25+18+10 gives us 53 also option B adds up to 53 whereas option C and option D add up to 74 and 68 hence option C and D cannot be the correct answer .Now we are left with option A and B so we have to check in this way in order to derive the final answer. As stated in the problem A gets Rs 7 more than B and B gets Rs 8 more than C.

(3) : A sum of Rs 2000 is divided into two parts such that one part is invested at 10% p.a and the second part at 15% p.a, after 2 years if Rs 460 is received as interest then ratio of investments of first and second part is?

A. 7:4

B. 4:3

**C. 7:3**

D. 6:4

**Solution:**Since total money is invested is Rs 2000,let us first check with option C and option D as only they add to 10 and we can easily find the two parts. Option C has ratio 7:3 hence the two parts are 1400 and 600 .10% on Rs 1400 for an year is Rs 140 and for two years, interest is Rs 280.15% on Rs 600 for two years is Rs 180.Now 180+280=Rs 460.

(4) : The students are in the ratio 2:3:5, if 20 students are increased in each class the ratio changes to 4:5:7.Find the total number in the three classes before the increase?

A. 309

**B. 100**

C. 117

D. 202

**Solution:**Here you have to check as if which option is divisible by 10 as the ratio stated in the problem add to 10 (2:3:5).

So you will find that only option D is divisible by 10 where as option A.B and C are not divisible by 10 so we need to omit out these three options .Now let the proportionate of students be 20:30:50 so the ratio add to 100. Now if 20 students are increased then it will become 40:50:70 thus the ratio we are getting as 4:5:7 which is mentioned in the above problem.