Explore Exams
Test Series
Live Tests
Prev. Papers
Quizzes
Live Quizzes
Current Affairs
News
Prepp+
GamesLogin / Register
All Exams Test series for 1 year @ ₹349 only
Question
JEE Main
Mathematics

A building construction work can be completed by two masons A and B together in 22.5 days. Mason A alone can complete the construction work in 24 days less than mason B alone. Then mason A alone will complete the construction work in :

The correct answer is
$36\text{ days}$

Mason A Alone Work Calculation

This problem involves calculating the time taken by Mason A to complete a construction work alone, given information about combined work time and the relative speeds of Mason A and Mason B.

Problem Setup

  • Let $d_A$ be the number of days Mason A takes to complete the work alone.
  • Let $d_B$ be the number of days Mason B takes to complete the work alone.
  • Given: A and B together complete the work in 22.5 days.
  • Given: Mason A alone completes the work in 24 days less than Mason B alone. This translates to the equation: $d_A = d_B - 24$, or $d_B = d_A + 24$.

Work Rate Equation

The rate at which work is done is the reciprocal of the time taken. The combined rate of A and B is the sum of their individual rates. The equation is:

$ \frac{1}{d_A} + \frac{1}{d_B} = \frac{1}{22.5} $

Solving for $d_A$

  1. Substitute $d_B = d_A + 24$ into the work rate equation: $ \frac{1}{d_A} + \frac{1}{d_A + 24} = \frac{1}{22.5} $
  2. Combine the fractions on the left side: $ \frac{(d_A + 24) + d_A}{d_A(d_A + 24)} = \frac{1}{22.5} $ $ \frac{2d_A + 24}{d_A^2 + 24d_A} = \frac{1}{22.5} $
  3. Cross-multiply: $ 22.5 \times (2d_A + 24) = d_A^2 + 24d_A $ $ 45d_A + 540 = d_A^2 + 24d_A $
  4. Rearrange into a quadratic equation: $ d_A^2 + 24d_A - 45d_A - 540 = 0 $ $ d_A^2 - 21d_A - 540 = 0 $
  5. Factor the quadratic equation. We need two numbers that multiply to -540 and add to -21. These numbers are -36 and 15. $ (d_A - 36)(d_A + 15) = 0 $
  6. Solve for $d_A$: The possible values for $d_A$ are $36$ or $-15$. Since time cannot be negative, we discard $-15$.

Conclusion

Therefore, Mason A alone will complete the construction work in 36 days.

Verification

If $d_A = 36$ days, then $d_B = d_A + 24 = 36 + 24 = 60$ days.

Combined work rate = $\frac{1}{36} + \frac{1}{60} = \frac{5}{180} + \frac{3}{180} = \frac{8}{180} = \frac{2}{45}$.

Time taken together = $\frac{1}{\text{Combined rate}} = \frac{1}{2/45} = \frac{45}{2} = 22.5$ days. This matches the given information.

Was this answer helpful?

Similar Questions

  1. Two distinct numbers $a$ and $b$ are selected at random from $1, 2, 3,..., 50$. The probability, that their product $ab$ is divisible by 3, is
    JEE Main
    Mathematics
    View Answer
  2. Let the mean and variance of 7 observations 2, 4, 10, x, 12, 14, y, $x > y$, be 8 and 16 respectively. Two numbers are chosen from $\{1, 2, 3, x-4, y, 5\}$ one after another without replacement, then the probability, that the smaller number among the two chosen numbers is less than 4, is :
    JEE Main
    Mathematics
    View Answer
  3. Let $S$ be a set of 5 elements and $\text{P}(S)$ denote the power set of $S$. Let $\text{E}$ be an event of choosing an ordered pair $(A, B)$ from the set $\text{P}(S) \times \text{P}(S)$ such that $A \cap B = \emptyset$. If the probability of the event $\text{E}$ is $\frac{3^p}{2^q}$, where $p, q \in \mathbb{N}$, then $p + q$ is equal to _______
    JEE Main
    Mathematics
    View Answer

Important Questions from Arithmetic

  1. Two distinct numbers $a$ and $b$ are selected at random from $1, 2, 3,..., 50$. The probability, that their product $ab$ is divisible by 3, is
    JEE Main
    Mathematics
    View Answer
  2. Let the mean and variance of 7 observations 2, 4, 10, x, 12, 14, y, $x > y$, be 8 and 16 respectively. Two numbers are chosen from $\{1, 2, 3, x-4, y, 5\}$ one after another without replacement, then the probability, that the smaller number among the two chosen numbers is less than 4, is :
    JEE Main
    Mathematics
    View Answer
  3. Let $S$ be a set of 5 elements and $\text{P}(S)$ denote the power set of $S$. Let $\text{E}$ be an event of choosing an ordered pair $(A, B)$ from the set $\text{P}(S) \times \text{P}(S)$ such that $A \cap B = \emptyset$. If the probability of the event $\text{E}$ is $\frac{3^p}{2^q}$, where $p, q \in \mathbb{N}$, then $p + q$ is equal to _______
    JEE Main
    Mathematics
    View Answer
Need Expert Advice?
More Questions from JEE Main
1)

Let A = {-3, -2, -1, 0, 1, 2, 3}. Let R be a relation on A defined by xRy if and only if $0\le x^2+2y\le 4$. Let $l$ be the number of elements in R and $m$ be the minimum number of elements required to be added in R to make it a reflexive relation. Then $l + m$ is equal to

2)

Let $\alpha$ and $\beta$ be the roots of $x^2 + \sqrt{3}x-16=0$, and $\gamma$ and $\delta$ be the roots of $x^2 + 3x - 1 = 0$. If $P_n = \alpha^n + \beta^n$ and $Q_n = \gamma^n + \delta^n$, then $\frac{P_{25} + \sqrt{3}P_{24}}{2P_{23}} + \frac{Q_{25}-Q_{23}}{Q_{24}}$ is equal to

3)

Let the domain of the function $f (x) = \log_2 \log_4 \log_6(3 + 4x -x^2)$ be $(a, b)$. 

If  $\int_{b-a}^{b+a}[x^2] dx=p-\sqrt{q}-\sqrt{r}$, $p,q,r\in N$, $gcd(p,q,r) = 1$, where $[.]$ is the greatest integer function, then $p + q + r$ is equal to

4)

Let A be a matrix of order $3 \times 3$ and $|A| = 5$. If $|2\text{adj} (3A \text{adj} (2A))| = 2^\alpha \cdot 3^\beta \cdot 5^\gamma$, $\alpha, \beta, \gamma \in N$, then $\alpha + \beta + \gamma$ is equal to

5)

Let $a_1, a_2, a_3,....$ be a G.P. of increasing positive numbers. If $a_3a_5 = 729$ and $a_2 + a_4 = \frac{111}{4}$, then $24 (a_1 + a_2 + a_3)$ is equal to

6)

The sum $1+3+11+25+45+71+ ...$ upto 20 terms, is equal to

7)
\[\sum_{r=1}^{9} \left( \frac{r+3}{2^{r}} \right).^{9}C_{r} = \alpha \left( \frac{3}{2} \right)  ^{9} - \beta\]

, $\alpha, \beta \in N$, then $(\alpha + \beta)^2$ is equal to

8)

The sum of all rational terms in the expansion of $(2+\sqrt{3})^8$ is

9)

The number of solutions of the equation $2x + 3\tan x = \pi$, $x \in [-2\pi, 2\pi]-\left\{ \pm \frac{\pi}{2}, \pm \frac{3\pi}{2} \right\}$ is:

10)

A line passing through the point $P(\sqrt{5}, \sqrt{5})$ intersects the ellipse $\frac{x^2}{36} + \frac{y^2}{25} = 1$ at A and B such that $(PA).(PB)$ is maximum. Then $5(PA^2 + PB^2)$ is equal to :

Start Your Preparation with Prepp Mobile App

Download the app from Google Play & App Store
Download the app from Google Play & App Store
Prepp Mobile App