College

1. Draw a whole line measuring 12 centimeters. Mark point C on it such that [tex]$x^2$[/tex] is [tex]$\frac{2}{1}$[/tex] of [tex]AR[/tex]. Mark point D such that [tex]DP[/tex] is [tex]$\frac{1}{4}$[/tex] of [tex]AC[/tex]. What is the value of 28?

2. A rectangular kite rope is cut into equal pieces. What is the length of three-quarters of one piece? How many centimeters is this?

3. Three liters of water are used to fill four identical bottles. One bottle is used to fill five identical cups. How much water is in one cup? How many milliliters is this?

4. A five-kilogram pumpkin is cut into five equal pieces. Each piece is further cut into two. What is the weight of each such piece? How many grams is this?

5. Calculate each of the following using multiplication:
- (i) [tex]\frac{3}{7}[/tex] of [tex]\frac{2}{5}[/tex]
- (ii) [tex]\frac{3}{5}[/tex] of [tex]\frac{2}{7}[/tex]
- (iii) [tex]\frac{2}{3}[/tex] of [tex]\frac{3}{4}[/tex]
- (iv) [tex]\frac{5}{6}[/tex] of [tex]\frac{3}{10}[/tex]

6. A bottle can hold one and a half liters of water. Four such bottles of water are poured into a jar. How much water is there in the jar? (Hint: Two bottles make three liters; four bottles make six liters. Here, we calculate 4 times [tex]$1 \frac{1}{2}$[/tex].)

Answer :

When we are given that a bottle can hold one and a half litres of water and we have four such bottles of water, we want to determine the total amount of water in the jar.

Let's break it down step-by-step:

1. Volume of a single bottle: We are told that one bottle can hold one and a half litres of water. In numerical terms, this is 1.5 litres.

2. Number of bottles: The total number of water bottles is four.

3. Total volume calculation: To find out how much water all the bottles together can hold, we multiply the volume of a single bottle by the number of bottles. That is:
[tex]\[
\text{Total Volume} = \text{Volume of one bottle} \times \text{Number of bottles}
\][/tex]
Substituting the values we know:
[tex]\[
\text{Total Volume} = 1.5 \text{ litres} \times 4 = 6 \text{ litres}
\][/tex]

Therefore, the total amount of water in the jar, when four bottles of water are poured into it, is 6 litres.

Summarizing:

- Each bottle holds: 1.5 litres
- Number of bottles: 4
- Total water in the jar: 6 litres