Ratio and Proportion for SSC CHSL questions

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Ratio and proportion was important topic for all competitive exams. The concepts to learn are less and the practice can improve your speed a lot, Mostly the questions are easily to solve and will be combined with other applications of ages, mixtures and proportions topics.

Ratio and Proportion for SSC CHSL:

You can practice SSC CHSL English question papers

Question 1:

By increasing the price of entry ticket to a fair in the ratio 9:13, the number of visitors to the fair has decreased in the ratio 7:4. In what ratio has the total collection increased or decreased?

a) increased in the ratio 52:63
b) increased in the ratio 36:91
c) decreased in the ratio 63:52
d) decreased in the ratio 91:36

Question 2:

If Giridhar’s salary is 5/3 times of Hariraj’s and Shaunak’s is 2/3 times of Hariraj’s, what is the ratio of Giridhar’s salary to Shaunak’s.

a) 9:10
b) 10:9
c) 5:2
d) 2:5

Question 3:

In an army selection process, the ratio of selected to unselected was 3:1. If 60 less had applied and 30 less selected, the ratio of selected to unselected would have been 5:1. How many candidates had applied for the process?

a) 240
b) 480
c) 120
d) 720

Question 4:

The bus fare between two cities is increased in the ratio 11:18. What would be the increase in the fare, if the original fare is Rs 550?

a) Rs 350
b) Rs 900
c) Rs 180
d) Rs 360

Question 5:

The third proportional of two numbers 4 and 28 is _______.

a) 52
b) 56
c) 84
d) 196

Question 6:

The third proportional of two numbers 9 and 15 is

a) 21
b) 30
c) 25
d) 45

Question 7:

The bus fare between two cities is increased in the ratio 25:29. Find the increase in the fare, if the original fare is Rs. 625

a) Rs 725
b) Rs 145
c) Rs 290
d) Rs 100

Question 8:

The third proportional of two numbers 24 and 36 is ?

a) 48
b) 54
c) 72
d) 108

Solutions (1 to 8)

Let cost of original ticket = Rs 9 and and number of visitors = 70
=> Original revenue = 9 $$\times$$ 70 = Rs 630
After increase in cost of ticket
New cost of ticket = Rs 13 and number of visitors = 40
=> New Revenue = 13 $$\times$$ 40 = Rs 520
Since, new revenue is less than original revenue, thus total collection has decreased.
$$\therefore$$ Decrease in total collection ratio = $$\frac{630}{520}$$ = 63 : 52
=> Ans – (C)

Let Hariraj’s salary = $$3x$$
=> Giridhar’s salary = $$\frac{5}{3} \times 3x = 5x$$
=> Shaunak’s salary = $$\frac{2}{3} \times 3x = 2x$$
$$\therefore$$ Ratio of Giridhar’s salary to Shaunak’s = $$\frac{5x}{2x}$$
= 5 : 2
=> Ans – (C)

Let $$4x$$ candidates applied for the process.
Candidates selected = $$3x$$ and candidates not selected = $$x$$
If candidates applied = $$4x – 60$$
Candidates selected = $$3x – 30$$
=> Candidates not selected = $$(4x – 60) – (3x – 30) = x – 30$$
According to ques,
=> $$\frac{3x – 30}{x – 30} = \frac{5}{1}$$
=> $$3x – 30 = 5x – 150$$
=> $$2x = 150 – 30 = 120$$
=> $$x = \frac{120}{2} = 60$$
$$\therefore$$ Number of candidates who applied for the process = $$4 \times 60 = 240$$
=> Ans – (A)

Let original fare = Rs. $$11x$$
=> New fare = Rs. $$18x$$
Also, original fare = $$550 = 11x$$
=> $$x = \frac{550}{11} = 50$$
$$\therefore$$ Increase in fare = $$18x – 11x = 7x$$
= $$7 \times 50 = Rs. 350$$

Three numbers a,b,c are in proportion iff $$b^2 = ac$$
Here, a = 4 and b = 28
=> $$(28)^2 = 4 \times c$$
=> $$c = \frac{28 \times 28}{4} = 7 \times 28$$
=> $$c = 196$$
=> Ans – (D)

Three numbers a,b,c are in proportion iff $$b^2 = ac$$ where $$b$$ is the mean proportion and $$c$$ is the third proportion
The given numbers are 9 and 15
=> $$(15)^2 = 9 \times c$$
=> $$c = \frac{15 \times 15}{9}$$
=> $$c = 5 \times 5 = 25$$
=> Ans – (C)

Let original fare = Rs. $$25x$$
=> New fare = Rs. $$29x$$
Also, original fare = $$625 = 25x$$
=> $$x = \frac{625}{25} = 25$$
$$\therefore$$ Increase in fare = $$29x – 25x = 4x$$
= $$4 \times 25 = Rs. 100$$

Three numbers a,b,c are in proportion iff $$b^2 = ac$$
=> $$(36)^2 = 24 \times c$$
=> $$c = \frac{36 \times 36}{24} = 3 \times 18$$
=> $$c = 54$$