The mass of equal volumes of gold and water are in the ratio 37 : 2. If 1 litre of water is 1 kg in mass, Class 8

The mass of equal volumes of gold and water are in the ratio 37 : 2. If 1 litre of water is 1 kg in mass, Class 8

Question 1.

The mass of equal volumes of gold and water are in the ratio 37 : 2. If 1 litre of water is 1 kg in mass, what is the mass of 1 litre of gold? Class 8

Solution:

Let mass of gold be 37x kg and that of water be 2x kg.

Volume of 1 kg water = 1 litre

So, volume of 2x kg water = 2x litres

It means 2x litres gold’s mass = 37x kg

i. e., 1 litre gold’s mass = [latex]\frac{37 x}{2 x}[/latex] kg

= [latex]\frac{37}{2}[/latex] kg

= 18[latex]\frac{1}{2}[/latex] kg

Question 2.

It is good farming practice to apply 10 tonnes of cow manure for 1 acre of land. A farmer is planning to grow tomatoes in a plot of size 200 ft by 500 ft. How much manure should he buy? (Please refer to the section on Unit Conversions earlier in this chapter). Class 8

Solution:

Area of the plot = 200 × 500

= 100000 sq. ft

= [latex]\frac{100000}{43560}[/latex] acres

So, manures to be bought

= [latex]\frac{100000}{43560}[/latex] × 10 tonnes

= 23 tonnes approx.