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A man, a boy and a woman can finish a work in 10 days, 15 days and 30 days, respectively. In how many days can the work be finished by a man, a woman and a boy when all of them work together?
To determine how long it takes for a man, a woman, and a boy to complete the work together, we first need to find their individual work rates.- The man's work rate is ( frac{1}{10} ) of the work per day.- The boy's work rate is ( frac{1}{15} ) of the work per day.- The woman's work rate is ( frac{1}Read more
To determine how long it takes for a man, a woman, and a boy to complete the work together, we first need to find their individual work rates.
– The man’s work rate is ( frac{1}{10} ) of the work per day.
– The boy’s work rate is ( frac{1}{15} ) of the work per day.
– The woman’s work rate is ( frac{1}{30} ) of the work per day.
Now, we add their work rates together:
[
text{Total work rate} = frac{1}{10} + frac{1}{15} + frac{1}{30}
]
To add these fractions, we need a common denominator, which in this case is 30.
[
frac{1}{10} = frac{3}{30}, quad frac{1}{15} = frac{2}{30}, quad frac{1}{30} = frac{1}{30}
]
Now, we can add them up:
[
text{Total work rate} = frac{3}{30} + frac{2}{30} + frac{1}{30} = frac{6}{30} = frac{1}{5}
]
This means that together, they complete ( frac{1}{5} ) of the work in one day. Therefore,
See lessIn what time will ₹10,000 at 4% per annum, produce the same interest as ₹8,000 does in 4 years at 5% simple interest?
To solve this, we first need to find the interest earned by ₹8,000 at 5% simple interest over 4 years.The formula for simple interest is:[ text{Interest} = frac{P times R times T}{100} ]Where:- ( P = 8000 ) (Principal)- ( R = 5 ) (Rate of interest)- ( T = 4 ) (Time in years)Calculating the interest:Read more
To solve this, we first need to find the interest earned by ₹8,000 at 5% simple interest over 4 years.
The formula for simple interest is:
[ text{Interest} = frac{P times R times T}{100} ]
Where:
– ( P = 8000 ) (Principal)
– ( R = 5 ) (Rate of interest)
– ( T = 4 ) (Time in years)
Calculating the interest:
[ text{Interest} = frac{8000 times 5 times 4}{100} ]
[ text{Interest} = frac{80000}{100} ]
[ text{Interest} = 800 ]
So, ₹8,000 at 5% over 4 years produces ₹800 in interest.
Now, we need to find out how much time it will take for ₹10,000 at 4% per annum to produce the same ₹800 in interest.
Using the simple interest formula again:
Let ( T ) be the time in years for ₹10,000 at 4% to produce ₹800 interest.
[ 800 = frac{10000 times 4 times T}{100} ]
[ 800 = 10000 times 0.04 times T ]
[ 800 = 400 times T ]
Now, solving for ( T ):
[ T
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The protocol used for controlling multimedia communication sessions is called SIP (Session Initiation Protocol).
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If there are n signal sources of the same data rate, then a TDM (Time Division Multiplexing) link has n slots.
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Time Division Multiplexing (TDM) is the technique that transmits digital signals.
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The Nobel Prize in 1901 for ‘recognition of the extraordinary services rendered by the discovery of the laws of chemical dynamics and osmotic pressure in solutions’ was awarded to Jacobus Henricus van 't Hoff.
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See lessThe sharing of a medium and its link by two or more devices is called _______
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