Dear Reader, Below are three problems dealing with ratios. You will find them useful for your preparation.
Question 1
Badri Prasad Sharma Constructions , Jalpaiguri, West Bengal was entrusted with construction work of a college hostel building meant for Scheduled Caste and Scheduled Tribe candidates. The foundation stone for construction of this building was laid by the Chief Minister of West Bengal Ms. Mamata Banerjee two months back. For construction of this building skilled men, skilled women and unskilled labourers were engaged in the ratio of 2:3:4 respectively. Daily wages was fixed at the rate of 5:3:2 for skilled men , skilled women and unskilled labourers respectively. For this project 100 unskilled labourers were engaged and proportionate number of skilled men and skilled women were engaged. The weekly wages for all of them accounted to Rs.405000.(Monday to Saturday). Find the daily wages of an unskilled labourer?
a) Rs. 300 b) Rs.500 c) Rs.175 d) Rs.200
Answer : d) Rs.200
Solution :
Number of unskilled labourers – 100.
Let the total number of labourers be L. Since skilled men, skilled women and unskilled labourers are in ratio 2:3:4, we can safely say that
4/ (2 + 3 + 4) x L = 100
4 / 9 x L = 100
L = 900/4 = 225.
Therefore number of men = 2 / (2 + 3 + 4) x L = 2 / 9 x 225 = 50
and number of women = 3 / (2 + 3 + 4) x L = 3/9 x 225 = 75
Now, lets assume skilled men are paid daily Rs. 5 each.
Since the ratio of the wages of the three groups is 5:3:2, then skilled woman will be paid Rs.3 and unskilled labourer will be paid Rs. 2.
Total wages paid to all of them will be
(50 x 5) + (75 x 3) + (100 x 2) = Rs.675 per day.
If they are paid this way weekly wages from monday to saturday will work out to Rs. 675 x 6 = Rs.4050.
Where the weekly wages is Rs.4050 for all of them – unskilled labourer is paid Rs.2
Total Weekly Wage Unskilled Labourer's Daily Wage 4050 2 405000 ?
Where the weekly wages is Rs.405000 – unskilled labourer will get 405000 x 2 / 4050 = Rs.200 per day.
Question 2
Excellent Electronics Limited is producing laptops. For manufacturing of these managers, supervisors and workers were engaged in the ratio 1: 3 : 6. Their salaries are in the ratio of 10: 4: 2. For this project 50 managers were engaged by the company. Proportionate number of supervisors and workers were also engaged. If managers are paid at the rate of Rs. 80000 per month. What is the total salary paid to all the managers, supervisors and workers put together per month?
a) Rs.10000000 b) Rs.13600000 c) Rs. 11200000 d) Rs.9600000
Answer : b) Rs. 13600000
Solution :
Number of managers:supervisors:labourers = 1:3:6
Number of managers – 50
Let us assume the sum of all people including managers, workers and supervisors be G.
Then number of managers = 1 / (1 + 3 + 6) x G = 50
Or G = 500
Number of supervisors = 3 / (1 + 3 + 6) x G = 3 x 500 / 10 = 150
Number of labourers = 6 / (1 + 3 + 6) x G = 6 x 500 / 10 = 300
Hence no. of manager, supervisors and labourers = 50, 150, 300
The salaries of managers, supervisors and labourers are in the ratio 10: 4: 2
Let S represents the sum of salary of 1 manager, 1 supervisor and 1 labourer
Its given that salary of each manager is 80000 per month.
Therefore 10 / (10 + 4 + 2) x S = 80000
Or S = 128000
Salary of each of the supervisors = 4 / (10 + 4 + 2) x S = 4 / 16 x 128000 = 32000 per month
Salary of each of the labourers = 2 / (10 + 4 + 2) x S = 2 / 16 x 128000 = 16000 per month
Since we already found that the no. of manager, supervisors and labourers = 50, 150, 300 , Total salary paid per month for all the employees =
(50 x 80000) + (150 x 32000) + (300 x 16000) = Rs.13600000
Question 3
In an Engineering College number of Professors: Lecturers: Asst. Lecturers is in the ratio 1: 8: 11. They are paid salary in the ratio 11:8:6. If the monthly salary of Asst. lecturers is Rs.24000 and number of Asst. Lecturers is 220, how much more salary does a Professor gets when compared to a Lecturer.
a) Rs.10000 b) Rs.12000 c) Rs.14000 d) None of these.
Answer : b) Rs. 12000
Solution :
Number of Asst. Lecturers – 220.
Let the total number of Professors, Lecturers and Asst. Lecturers be P
Also, Professors: Lecturers: Asst. Lecturers is in the ratio 1: 8: 11
Therefore 11 / ( 1 + 8 + 11) x P = 220
Or P = 220 x 20/11 = 400
Number of Lecturers - 8 / ( 1 + 8 + 11) x P = 8 / 20 x 400 = 160
Number of Professors - 1 / ( 1 + 8 + 11) x P = 1 / 20 x 400 = 20
Let S represent the sum of salaries of a Professor, Lecturer and Assistant Lecturer.
Ratio of their salaries = 11:8:6
It is given that, Salary of Asst. Lecturers - Rs.24000 p.m.
Therefore, 6 / (11 + 8 + 6) x S = 24000
Or S = 24000 x 25 / 6 = 100000
Now we have to find the difference in salaries of a Professor and Lecturer
Salary of a Professor = 11 / (11 + 8 + 6) x S
Salary of a Lecturer = 8 / (11 + 8 + 6) x S
Salary of Professor - Salary of a Lecturer = 11 / (11 + 8 + 6) x S - 8 / (11 + 8 + 6) x S = 3 / (11 + 8 + 6) x S = 3 / (11 + 8 + 6) x 100000 = Rs 12000 per month.