Quantitative Aptitude
TIME AND WORK MCQs
Time & Work, Work And Wages
(A + B + C)'s 1 day's work = \(\frac{1}{6}\)
(A + B)'s 1 day's work = \(\frac{1}{8}\)
(B + C)'s 1 day's work = \(\frac{1}{12}\)
So , (A + C)'s 1 day's work = \(\left(2\times \frac{1}{6}\right)-\left(\frac{1}{8}+\frac{1}{12}\right)\)
= \(\left(\frac{1}{3}-\frac{5}{24}\right)\)
= \(\frac{3}{24}\)
= \(\frac{1}{8}\)
So, A and C together will do the work in 8 days.
(B + C)'s 1 day's work = \(\left(\frac{1}{9}+\frac{1}{12}\right)=\frac{7}{36} \)
Work done by B and C in 3 days = \(\left(\frac{7}{36}\times3\right)=\frac{7}{12} \)
Remaining work = \(\left(1-\frac{7}{12}\right)= \frac{5}{12}\)
Now, \(\frac{1}{24} \) work is done by A in 1 day.
So, \(\frac{5}{12}\) work is done by A in \(\left(24\times\frac{5}{12}\right)= 10 days.\)
Work done by X in 8 days = \(\left(\frac{1}{40}\times8\right)=\frac{1}{5}\)
Remaining work = \(\left(1-\frac{1}{5}\right)=\frac{4}{5}\)
Now, \(\frac{4}{5}\) work is done by Y in 16 days.
Whole work will be done by Y in \(\left(16\times\frac{5}{4}\right)= 20 days.\)
So, X's 1 day's work = \(\frac{1}{40}\) , Y's 1 day's work = \(\frac{1}{20}\)
(X + Y)'s 1 day's work = \(\left(\frac{1}{40}+\frac{1}{20}\right) = \frac{3}{40}\)
Hence, X and Y will together complete the work in \(\left(\frac{40}{3}\right) = 13\frac{1}{3}days.\)
(A's 1 day's work) : (B's 1 day's work) = \(\frac{7}{4}:1 = 7:4\)
Let A's and B's 1 day's work be 7x and 4x respectively.
Then, 7x + 4x = \(\frac{1}{7}\Rightarrow 11x =\frac{1}{7}\Rightarrow x=\frac{1}{77}\)
So, A's 1 day's work = \(\left(\frac{1}{77}\times7\right) = \frac{1}{11}\)
Let A's 1 day's work = x and B's 1 day's work = y.
Then , x+y = \(\frac{1}{30}\) and 16x + 44y = 1.
lving these two equations, we get: x = \(\frac{1}{60}\) and y = \(\frac{1}{60}\)
Therefore , B's 1 day's work = \(\frac{1}{60}\)
Hence, B alone shall finish the whole work in 60 days.
Let the daily wage of a man, a woman, and a boy be m, w, and b, respectively.
From the given statement, we can form the following equations:
5m = w (because 5 men are equal to as many women)w = 8b (because as many women are equal to 8 boys)
Substituting the second equation in the first, we get:
5m = 8b
Or, m = (8/5)b
Now, we can write the total daily wage as:
5m + w + 8b = 90
Substituting the value of w from the second equation, we get:
5m + 8b + 8b = 90
Or, 5m + 16b = 90
Substituting the value of m from the earlier equation, we get:
5(8/5)b + 16b = 90
Or, 8b + 16b = 90
Or, 24b = 90
Or, b = 90/24 = 15/4
Substituting the value of b in the equation for m, we get:
m = (8/5) x (15/4) = 6
Therefore, the daily wage of a man is Rs 6, which is option (C).
Let's assume the daily wage of the worker to be x.
Total wage for n days = n*x
Given, the worker is engaged for a certain number of days for Rs 1725, therefore we have:
n*x = 1725 ...(1)
Now, the worker was absent for 7 days, so the total number of days worked would be (n-7).
Given, the worker was paid Rs 920, so we have:
(n-7)*x = 920 ...(2)
On solving equations (1) and (2), we get:
n = 23 and x = 75
Therefore, the daily wage of the worker is Rs 75.
Explanation:
Let's assume the daily wage of the worker to be x.
The total wage paid for n days is given as Rs 1725. Therefore, we get the equation:
n*x = 1725
The worker was absent for 7 days. Therefore, the total number of days worked by the worker is (n-7). The amount paid to the worker is given as Rs 920. Therefore, we get the equation:
(n-7)*x = 920
On solving the above two equations, we get:
n = 23 and x = 75
Therefore, the daily wage of the worker is Rs 75.
Some relevant definitions and formulas used in the solution are:
Linear equation: An equation of the form "ax + b = c", where "a", "b", and "c" are constants and "x" is a variable.
System of linear equations: Two or more linear equations with the same variables.
Substitution method: A method for solving a system of linear equations by solving one equation for one variable and substituting the result into the other equation(s).
Variable: A symbol or letter used to represent an unknown quantity in an equation or expression.
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