A digital watch X beeps every 30 seconds while watch Y beeps every 32 seconds. They beeped together at 10 AM. The immediate next time that they will beep together is ________
Determine Next Simultaneous Beep Time
Watch X beeps every 30 seconds, and watch Y beeps every 32 seconds. They beeped together at 10 AM. We need to find the immediate next time they will beep simultaneously.
Calculate LCM of Beep Intervals
To find the next simultaneous beep time, we calculate the Least Common Multiple (LCM) of the beep intervals, which are 30 seconds and 32 seconds. The LCM gives the minimum time interval after which both watches will beep at the same moment.
Find the prime factorization for each interval:
- $30 = 2 \times 3 \times 5$
- $32 = 2^5$
Calculate the LCM using the highest power of each prime factor:
LCM$(30, 32) = 2^5 \times 3 \times 5 = 32 \times 15 = 480$ seconds.
Determine Next Beep Time
The watches will beep together again after 480 seconds.
Convert the LCM from seconds to minutes:
$480 \text{ seconds} = \frac{480}{60} \text{ minutes} = 8 \text{ minutes}$
They last beeped together at 10 AM. Add the calculated interval to find the next simultaneous beep time:
Next Beep Time = 10:00 AM + 8 minutes = 10:08 AM.
Important Questions from Numerical Computation
- An organization allows its employees to work independently on consultancy projects but charges an overhead on the consulting fee. The overhead is 20% of the consulting fee, if the fee is up to . 5,00,000. For higher fees, the overhead is . 1,00,000 plus 10% of the amount by which the fee exceeds . 5,00,000. The government charges a Goods and Services Tax of 18% on the total amount (the consulting fee plus the overhead). An employee of the organization charges this entire amount, i.e., the consulting fee, overhead, and tax, to the client. If the client cannot pay more than . 10,00,000, what is the maximum consulting fee that the employee can charge?
Three frictionless pulleys with rope attachment are in a static equilibrium as shown in the figure. The mass $m_1$ and $m_2$, in kg, respectively are
If the in-situ density of coal is 1320 kg/m$^3$ and the density of blasted coal is 952 kg/m$^3$, the swell factor is _____________ (rounded off to 3 decimal places)
A five-member truss system is shown in the figure. The maximum vertical force P in kN that can be applied so that loads on the member CD and BC do NOT exceed 50 kN and 30 kN, respectively is _____________(rounded off to 2 decimal places)
The Fourier transform and its inverse transform are respectively defined as $\tilde{f}(\omega) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{+\infty} f(x)e^{i\omega x}dx$ and $f(x) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{+\infty} \tilde{f}(\omega)e^{-i\omega x}d\omega$. Consider two functions $f$ and $g$. Another function $f * g$ is defined as
$(f * g)(x) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{+\infty} f(y)g(x - y)dy$
Which of the following relation is/are true?
Note: Tilde ($\sim$) denotes the Fourier transform.
