Figure out solutions to these sums

Hyderabad: This article is in continuation to the last article focusing on the ratio and proportion topic. Here are some practice questions along with solutions on the ratio and proportion topic that will help you in your preparation for the State government recruitment jobs.

A person invested some amount in two schemes A and B in the ratio of X : Y respectively and received equal interest from both the schemes after three years. If the rate of simple interest in both the schemes A and B are in the ratio of 7 : 5, then find the value of X : Y.

a) 4 : 7 b) 5 : 6 c) 5 : 7 d) 5 : 4

Ans: c

Solution: Let, the rate of interest in scheme A be 7x and scheme B be 5x
∴ X × 3 × 7X/100 = Y × 3 × 5X/100

X/Y = 5/7
The monthly income of A and B are in the ratio of 3 : 4 respectively and the monthly saving of A, B, and C are in the ratio of 4: 5: 6 respectively. The monthly expenditure of A is Rs 2,500 less than that of C and the monthly expenditures of B is Rs.1000 more than that of A. Every month, C spends Rs 5,000 then how much money does he save?
a) Rs 2,000 b) Rs 2,500 c) Rs 3,000 d) Rs 3,500

Ans: c

Solution: Let the income of A = 3x then the income of B = 4x

The expenditures of C = 5000
The expenditures of A = 5000 – 2500 = 2500
The expenditures of B = 2500 1000 = 3500
Let us consider the ratio of A and B on 3x – 2500 / 4x – 3500 = 4/5
15x – 12500 = 16x – 14000

x = 1500

The saving of A = 3x – 2500 = 4500 – 2500 = 2000 = 4y

y = 500
The saving of C = 6y = 6 × 500 = 3000
The number of employees in a company is reduced in the ratio 3 : 2 and the salary of each employee is increased in the ratio 4 : 5. By doing so, company saves Rs 12,000. Find the initial expenditure of the company on salary.
a) Rs 52000 b) Rs 62000 c) Rs 72000 d) Rs 82000

Ans: c

Solution: Let the number of employees earlier = ‘3a’
Then, number of employees now = ‘2a’.

∵ Average salary of employees earlier = ‘4b’,

∴ Average salary of employees now = ‘5b’.

⇒ Total salary of employees earlier = 3a × 4b = 12ab
⇒ Total salary of employees now = 2a × 5b = 10ab

∴ Difference = 12ab – 10ab = 2ab
Given that,

⇒ 2ab = Rs 12,000

Then, initial expenditure = 12ab = 2ab × 6 = Rs 72000

The average age of four friends Reena, Sandhya, Yamini and Sujata is 21 years. The sum of the age of Reena and Sandhya is 14 years more than the age of Sujata. The difference between the age of Sujata and Sandhya is 4 years. The difference between the age of Sujata and Reena is 6 years. Find the average age of Reena, Sandhya and Yamini after 3 years.

a) 20 years b) 21 years c) 23 years d) 25 years

Ans: c

Solution: Let the present age of Reena, Sandhya, Yamini and Sujata be R, Sa, Y and Su respectively.

R Sa Y Su = 21 × 4 = 84 years …(i) R Sa = Su 14 …(ii)

Su – Sa = 4 Sa = Su – 4

Su – R = 6

R = Su – 6

Put the value of R and Sa in (ii)

Su – 6 Su – 4 = Su 14

Su = 24 years

R = 18 years

Sa = 20 years

From (i), Y = 22 years

Average age after 3 years 18 3 20 3 22 3 / 3

= 23 years

Marks obtained by Mohan in Hindi and English are in the ratio of 4 : 5, respectively, while ratio of marks obtained by Mohan in Maths and Science is 5 : 6, respectively. He scored 36 marks more in Science than in English, and 32 marks more in Maths than in Hindi. Find the ratio of marks obtained by Mohan in Hindi and Science.
a) 1 : 2 b) 2 : 3 c) 4 : 5 d) 5 : 6
Ans: a

Solution: Let, marks obtained by Mohan in Hindi and English be 4x and 5x, respectively

And, marks obtained by Mohan in Maths and Science be 5y and 6y, respectively

So, 6y – 5x = 36 5x/6 = 6

And 5y – 4x = 3

5 × (36 5x / 6) – 4x = 32

180 25x – 24x = 192 x = 12

So, y = 96/6

Required ratio = 4x : 6y = 4 × 12 : 6 × 16 = 48 : 96 = 1 : 2