Ratio and Proportion

A politician inspecting a school asked the students -"There are 30 students in this class and my monthly salary is Rs. 12000. So what is my age?" All students were puzzled how to solve this problem. Then one student said -"Sir, your age is 40 years". Now the politician was puzzled. "How did you find out my correct age?", he asked. The student replied -"Sir, my elder brother is half mad and he is 20 years old".

        Well, that is an example of unitary method, using direct proportion.

• Two quantities of same kind measured in same units can be compared by difference or by division. Ratio of a number a to b is the quotient a/b and is written as a : b. Usually a ratio is written in simplest form or lowest terms.
• If ratios a : b and b : c are given, then a : c can be calculated from
•   a/c = (a/b) × (b/c)
• Four numbers a, b, c, d are said to be in proportion if the ratios a : b and c : d are equal, that is if a/b = c/d, that is if ad = bc. This is known as cross product rule.
• Three numbers a, b, c are in continued proportion if ratios a : b and b : c are equal, that is if b² = ac.
• In unitary method of solving arithmetic problems, we find the time, price etc. for a unit (one) item. However we have to first see whether there is direct proportion or inverse proportion.

Exercise

1. 5 grams of an alloy contains 3¾ grams copper and rest is nickel. Find the ratio of weights of nickel and copper.
2. Verify that 18, 27, 20, 30 are in proportion. Set up all possible proportions between these four numbers.
3. Bananas are selling at Rs 15 a dozen. How many bananas would you get for ten rupees?
4. It rained 80 mm in first 20 days of April. What would be the total rainfall in April?
5. Two numbers are in ratio 6:5. If the first number is halved and 2 is subtracted from second, they are in ratio 2:3. Find the numbers.
6. A dozen eggs cost 15 rupees. How much would a hundred eggs cost?
7. 50 grams of fish food is sufficient for 8 fish for a day. How much food would 12 fish require in a day?
8. 50 grams of fish food is sufficient for 8 fish for a day. On the same amount of food, for how many days can 2 fish survive?

Answers