Maths-
General
Easy
Question
A, B and C can reap a field in 15 ¾ days; B, C and D in 14 days; C, D and A in 18 days; D, A and B in 21 days. In what time can A, B, C and D together reap it?
Hint:
Hint:
When two quantities of different units are compared and expressed as a ratio, it is known as Rate. For example, a car travels at a speed of 100 kilometres per hour, then it means in one hour it covers 100 kilometres.
The correct answer is: 12 3/5 days
Let’s say the total work done to reap the field is represented as W and let’s say the work done by A in 1 day is WA, work done by B in 1 day is WB,work done by C in 1 day is WC and work done by D in 1 day is WD
Step 1 of 3:
It is given that A, B and C can reap a field in 15 ¾ days or 15.75 days. So we can write
WA
15.75 + WB
15.75 + WC
15.75 = W
WA + WB + WC =
…….(1)
It is given that B, C and D can reap a field in 14 days. So we can write
WB
14 + WC
14 + WD
14 = W
WB + WC + WD =
…….(2)
It is given that C, D and A can reap a field in 18 days. So we can write
WC
18 + WD
18 + WA
18 = W
WC + WD + WA =
…….(3)
It is given that D, A and B can reap a field in 21 days. So we can write
WC
21 + WD
21 + WA
21 = W
WD + WA + WB =
…….(4)
Step 2 of 3:
Now, adding equations (1), (2), (3) and (4)
3(WA + WB + WC + WD) = ![fraction numerator W over denominator 15.75 end fraction plus W over 14 plus W over 18 plus W over 21](data:image/png;base64,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)
WA + WB + WC + WD =
……(4)
Step 3 of 3:
Let’s say the time taken by all of them to complete the work is t. So we can write
WA
t + WB
t + WC
t + WD
t = W
t(WA + WB + WC + WD) = W
Using equation (4)
t ![cross times](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAKCAYAAABSfLWiAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAAC1JREFUeNpjYMAE1VDMQKIcUYpJMgCbJrIMQDZoNyUGUMUQir1DccBSLYrpDwAMJw7rHduE6QAAAE50RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+JiN4RDc7PC9tbz48L21hdGg+HjBxXgAAAABJRU5ErkJggg==)
= W
t =
days = 12
days.
Final Answer:
Hence, the time taken by A, B, C and D together to reap the field is 12
days.
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Maths-General
Maths-
Approximate the following irrational numbers to the nearest whole number.![square root of 28](data:image/png;base64,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)
Approximate the following irrational numbers to the nearest whole number.![square root of 28](data:image/png;base64,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)
Maths-General