Example 1
₹60 is shared between Asha and Ben in the ratio 2 : 3. How much does Asha get?
- First share = total × first term ÷ sum of the terms
- = 60 × 2 ÷ (2 + 3) = 120 ÷ 5
- = ₹24
Answer: ₹24
Ratio and Proportion Questions with Solutions
Ratio and proportion with worked examples: sharing in a ratio, the fourth proportional and partnership profit, solved step by step, with free practice.
How to solve ratio and proportion questions
Share in a ratio
To split a total in the ratio a : b, add the terms. The first share is total × a ÷ (a + b).
Fourth proportional
If a : b = c : x, the products of the outer and inner terms are equal, so x = b × c ÷ a.
Partnership share
Partners share profit in the ratio of money × months. A share is total × that partner's money × months ÷ the sum for all partners.
Worked examples
Example 2
What is the fourth proportional to 2, 6 and 5?
- If 2 : 6 = 5 : x, then 2 × x = 6 × 5
- x = 6 × 5 ÷ 2 = 30 ÷ 2
- x = 15
Answer: 15
Example 3
Anil puts ₹5000 into a business for 12 months and Bina puts in ₹3000 for 8 months. They earn a profit of ₹1400. What is Anil's share of the profit?
- Anil : Bina = 5000 × 12 : 3000 × 8 = 60000 : 24000 = 5 : 2
- Anil's share = 1400 × 5 ÷ (5 + 2) = 7000 ÷ 7
- = ₹1000
Answer: ₹1000