Formulas for Ratio and Proportions

Question 1 : Sales manager of pepperfry.com was checking the inventory and concluded that the cost price of 2 tables and 3 chairs is Rs. 2200 and the cost price of 2 chairs and 4 tables is Rs. 2400. The question is what will be the ratio between the cost price of the chairs and the table ? 

Options :

1. 8 : 9
2. 6 : 5
3. 9 : 5
4. 10 : 7

Answer: d.

Options : 

1. 2450 Rs
2. 4552 Rs
3. 1150 Rs
4. 4598 Rs

Answer: b.

Solution : Let the income of Kate in 2018 and 2017 be 3x and 5x respectively.
Let the income of Jennifer in 2018 and 2017 be 3y and 2y respectively
Since, the ratio of their income in the year 2017 was 5 : 4
5x : 2y = 5 : 4
2x = y
The sum of their incomes in 2018 is Rs. 10242
3x + 3y = 10, 242
9x = 10, 242
x = 1,138 and y = 2276
Jennifer’s income for the year 2017 = 2y = Rs. 4552

Question 3 : Rick Grimes has 2 vessels A and B of equal volume containing Petrol and Diesel in the ratio 3 : 2 and 2 : 1 to their brim respectively. He then poured two litres of the solution from vessel A and three litres of the solution from vessel B into a big empty vessel C. If the solution in C occupied 40% of the capacity of C, what proportion would he achieve of the volume of vessel C which should be the volume of Diesel that shall be added so that the ratio of Petrol and Diesel in vessel C becomes 1 : 1?

Options : 

1. 21 : 152
2. 22 : 120
3. 14 : 125
4. 14 : 150

Answer: c.

Solution : Amount of Petrol poured into C from vessel A and B,
=2\times \frac{3}{5}+3\times \frac{2}{3}=\frac{16}{5}litres

Also, amount of Diesel poured into C from vessels A and B,
=5-\frac{16}{5}=\frac{9}{5}litres

Given, 5 litres rePresent 40% of the capacity of vessel C, vessel C has a capacity of,
=5\times \frac{5}{2} = 12.5 litres

To make the quantities of Diesel and Petrol same in the vessel C, quantity of Diesel to be added,
=\frac{16}{5}-\frac{9}{5}= \frac{7}{5} litres

Therefore, the required ratio is,
=\frac{\frac{7}{5}}{12.5}= \frac{14}{125}litres

Question 4: Vin Diesel distributed some chocolates among his four children and kept some with him. The eldest three children got chocolates in the ratio 3 : 11 : 7. The total number of chocolates with Vin and youngest child is three times the total chocolates with the three eldest children. The ratio of chocolates with Vin and that with all the children is 3 : 4. Find the total number of chocolates if the youngest child has 81 chocolates with him?
Options : 

1. 252
2. 263
3. 274
4. 285

Answer: a.
Solutions : Let the children be P, Q, R and S and Mr Flynn be F

Chocolates with P : Q : R = 3 : 7 : 11

Let the number of chocolates be 3X, 7X and 11X

Total chocolates with three eldest children = 21X

Chocolate with F and S = 3 × 21X = 63X

Total chocolates = (21X + 63X) = 84X

Chocolate with F : (P + Q + R + S) = 3 : 4

Total 7 units of chocolate = 84 X

1 unit = 12X

Chocolate with F = 3 × 12X = 36X

Chocolate with S =  (63X – 36X) = 27X

27 X = 81  →  X=3 

Total number of chocolates = 84X = 84 × 3 = 252

Question 5 : Tyris Gibson has scored the marks which are in the ratio of 7 : 10 in theory exams. Total marks which can be obtained in practicals were 20% of the total marks of theory. If Tyris got full marks in practical then find the ratio of total marks obtained by Tyris to the total marks which can be obtained in the subject.
Options :

1. 4 : 5
2. 3 : 5
3. 2 : 4
4. 3 : 4

Answer: d.
Solution : Let, marks obtained by Tyris Gibson in theory and total marks of theory be ‘7x’ and ‘10x’ respectively

So, total marks (theory + practical) = 10x + 2x = 12x

Marks obtained by Tyris Gibson (theory + practical) = 7x + 2x = 9 x

Required Ratio = \frac{9x}{12x}=\frac{3}{4}