Madhya Pradesh Board Solutions for Chapter: Direct and Inverse Proportions, Exercise 2: EXERCISE

A photograph of a bacteria enlarged $\mathrm{50,000}$ times attains a length of $5 \mathrm{c}\mathrm{m}$ as shown in the diagram. What is the actual length of the bacteria? If the photograph is enlarged $\mathrm{20,000}$ times only, what would be its enlarged length?

In a model of a ship, the mast is $9 \mathrm{c}\mathrm{m}$ high, while the mast of the actual ship is $12 \mathrm{m}$ high. The length of the actual ship is $28 \mathrm{m}$, if the model ship is $k \mathrm{cm}$, then find the value of $k.$

Suppose $2 \mathrm{kg}$ of sugar contains $9\times {10}^6$ crystals. If there are $m\times {10}^7$ sugar crystals in $5 \mathrm{kg}$ of sugar, then find the value of $m$.

Suppose $2 \mathrm{kg}$ of sugar contains $9\times {10}^6$ crystals. If there are $m\times {10}^n$ sugar crystals in $1.2 \mathrm{kg}$ of sugar, then find the value of $m+n$.

Rashmi has a road map with a scale of $1 \mathrm{c}\mathrm{m}$ representing $18 \mathrm{k}\mathrm{m}$. She drives on a road for $72 \mathrm{k}\mathrm{m}$. What would be her distance covered in the map $\left(\mathrm{in} \mathrm{cm}\right)$?

A $5 \mathrm{m} 60 \mathrm{c}\mathrm{m}$ high vertical pole casts a shadow $3 \mathrm{m} 20 \mathrm{c}\mathrm{m}$ long. If at the same time the length of the shadow cast by another pole $10 \mathrm{m} 50 \mathrm{c}\mathrm{m}$ high is $x \mathrm{m}$, then find the value of $x$.

A $5 \mathrm{m} 60 \mathrm{c}\mathrm{m}$ high vertical pole casts a shadow $3 \mathrm{m} 20 \mathrm{c}\mathrm{m}$ long. Find at the same time the height of a pole (in $\mathrm{m}$) that casts a shadow $5 \mathrm{m}$ long.

A loaded truck travels $14 \mathrm{km}$ in $25 \mathrm{minutes}.$ If the speed remains the same, it can travel $k \mathrm{km}$ in $5 \mathrm{hours}$, then find the value of $k.$