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Question

Answers

A) 15.6 seconds

B) 9 seconds

C) 1.3 minutes

D) 78 minutes

Answer

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While using the unitary method, we have to find the amount needed for one unit of the substance and then we multiply by the quantity provided.

For example, if 3 boxes can be filled by 12 chocolates, 1 box will be filled by 4 chocolates and hence 5 jugs will be filled by 20 chocolates. It is simply done by calculating multiplication $5 \times 4$.

Step 1:

1 megabytes $ = \mathop {{\text{10}}}\nolimits^{\text{6}} {\text{ }}$bytes

Step 2:

Also, \[\mathop {{\text{10}}}\nolimits^{\text{6}} {\text{ }}\]bytes = 1 megabytes

Hence, ${\text{1 byte=}}\dfrac{{\text{1}}}{{\mathop {{\text{10}}}\nolimits^{\text{6}} }}{\text{ megabytes}}$

$2340 \times 10^6 \text{bytes} = 2340 \times 10^6 \times \dfrac{1}{10^6} \text{megabytes}$

= 2,340 megabytes …… (1)

Step 3:

The rate at which the information is accessed on the computer = 150 megabytes per second

($\because $given)

$ \Rightarrow $In one second, 150 megabytes of information is accessed on the computer.

Or, 150 megabytes of information is accessed in = 1 sec

1 megabyte of information is accessed in $ = \dfrac{1}{{150}}$sec

2,340 megabytes of information is accessed in $ = 2,340 \times \dfrac{1}{{150}}{\text{ sec}}$

$

{\text{ =2,34{0}}} \times \dfrac{1}{{15{0}}}{\text{ sec}} \\

{\text{ =}}\dfrac{{234}}{{15}}{\text{ sec}} \\

$

${\text{ =15}}{\text{.6 sec}}$…… (2)

Step 4:

Size of one file$ = 2,340 \times \mathop {10}\nolimits^6 $bytes($\because $given)

= 2,340 megabytes(from (1))

Step 5:

Time to access one file on computer = 15.6 sec(from (2))

Time to access five files on computer $ = 5 \times 15.6{\text{ sec}}$

= 78 sec

Step 6

1 minutes = 60 seconds

Or, 60 seconds = 1 minutes

${\text{1 seconds=}}\dfrac{{\text{1}}}{{{\text{60}}}}{\text{ minutes}}$

$\therefore {\text{78 seconds=}}\dfrac{{{\text{78}}}}{{{\text{60}}}}{\text{ minutes}}$

= 1.3 minutes

Step 7

Time to access five files on computer = 78 sec = 1.3 minutes.

The final answer should be in the simplest fraction. A fraction is said to be the simplest (or lowest) if its numerator or denominator has no common factor except for 1.

While dividing two numbers, make sure their units are the same.

To convert minutes into seconds, it is multiplied by 60.

Interconversion unit’s example:

Convert 7 minutes into seconds

Sol: 1 minutes = 60 seconds

$7$ minutes = $7 \times 60$ seconds

=420 seconds