Question

First pipe can fill a tank in 12 hours. second pipe can fill the same tank in 6 hours. third • pipe in 4 hours. how long will it take to fill the tank if all the 3 pipes are opened simultaneously?find the greatest number that will divide 43, 91 and 18~ so as to leave the same remainder in each case

Answer 1

First pipe fills a tank in 12 hours
In 1 hour it fills: 1/12 part of the tank
Second pipe fills the tank in 6 hours
In 1 hour, it fills: 1/6 part of tank
Third pipe fills the tank in 4 hours
In 1 hour, it fills: 1/4 part of tank

All the three together in 1 hour fills:
1/12 + 1/6 + 1/4 = 1+2+3/12 = 6/12 = 1/2 part
1 hour===1/2 part
X hours=== 1 part
X = 2 hours.
Hence, all the three pipes opened together, the tank gets filled in 2 hours.

Greatest number that divides 43, 91, 18 to leave same remainders.
Find the HCF of difference between the numbers.
91 - 43 = 48
43 - 18 = 25
91 - 18 = 73
Here the HCF of (48,25,73) is '1'... So please check the question part to see if you have misplaced (mis represented) any number. Hope you have understood the method for this(HCF) question. In case, if any number was entered wrongly, correct it and try it yourself based on above approach.
Hope it helps

Answer 2

Concept introduction:

Time is the continuous sequence of events and presence that reportedly happens in an irrevocable order from the past through into the present and into the future.

Given:

Here it is given that ,

• First pipe can fill a tank in $12$ hours.
• Second pipe can fill the same tank in $6$ hours.
• Third pipe can fill the tank in $4$ hours.

To find:

We have to find how long will it take to fill the tank if all the $3$ pipes are opened simultaneously and find the greatest number that will divide $43, 91$and $18$ so as to leave the same remainder in each case.

Solution:

According to the question,

First pipe fills a tank in $12$ hours

In $1$ hour it fills: $1/12$ part of the tank

Second pipe fills the tank in $6$ hours

In $1$ hour, it fills: $1/6$ part of tank

Third pipe fills the tank in $4$ hours

In $1$ hour, it fills: $1/4$ part of tank

All the three together in $1$ hour fills:

$1/12 + 1/6 + 1/4 \\= 1+2+3/12\\ = 6/12 = 1/2$ part

$1$ hour$=1/2$ part

$X$ hours$= 1$ part

$X = 2$ hours.

Greatest number that divides $43, 91, 18$ to leave same remainders.

Find the HCF of difference between the numbers.

$91 - 43 = 48\\43 - 18 = 25\\91 - 18 = 73$

Here the HCF of $(48,25,73)$ is $'1'$.

Final answer:

The final answers of these questions are $(i) 2$ hours and $(ii) 1$.

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