Example 3: Leena made 5 cups of tea. She used 1⁄4 litre of milk for this. How much milk is there in each cup of tea?
Answer
One-quarter litre of milk is shared equally by 5 cups.
Milk per cup = 1/4 ÷ 5
Reciprocal of 5 is 1/5
= 1/5 × 1/4
= 1/20 litre = 50 ml
Why it happens: 5 × (milk per cup) must be 1⁄4 litre. Twenty such cups would use one full litre, so each cup holds 1⁄20 litre.
Q2.
Example 4: Here is an example from Baudhāyana’s Śhulbasūtra (c. 800 BCE). Cover an area of 7 1⁄2 square units with square bricks each of whose sides is 1⁄5 units. How many such square bricks are needed?
Answer
Find the area of one brick first.
Area of one brick = 1/5 × 1/5 = 1/25 square units
Total area = 7 1/2 = 15/2 square units
Number of bricks = 15/2 ÷ 1/25
Reciprocal of 1/25 is 25
= 25 × 15/2
= 375/2 = 187 1/2 bricks
Did you know? The answer really is 187½ — the Śhulbasūtra builders cut bricks in half while laying fire altars, so half-bricks were perfectly normal for them.
Q3.
Example 5: Four fountains fill a cistern. The first fountain can fill the cistern in a day. The second can fill it in half a day. The third can fill it in a quarter of a day. The fourth can fill the cistern in one fifth of a day. If they all flow together, in how much time will they fill the cistern? In a day, the number of times — the first fountain will fill the cistern is 1 ÷ 1 = 1; the second is 1 ÷ 1⁄2 = ____; the third is 1 ÷ 1⁄4 = ____; the fourth is 1 ÷ 1⁄5 = ____. The number of times the four fountains together will fill the cistern in a day is ___ + ___ + ___ + ___ = 12.
Answer
Count how many cisterns each fountain fills in one full day.
Fountain
Time for one filling
Fillings in a day
First
1 day
1 ÷ 1 = 1
Second
1/2 day
1 ÷ 1/2 = 2
Third
1/4 day
1 ÷ 1/4 = 4
Fourth
1/5 day
1 ÷ 1/5 = 5
Together in a day = 1 + 2 + 4 + 5 = 12 fillings
Time for 1 filling = 1 ÷ 12
= 1/12 day = 2 hours
Why we add the rates, not the times: the four fountains pour at the same moment, so their speeds add up. Twelve cisterns a day means one cistern in a twelfth of a day.