Certificates / Quantitative aptitude / Ratio and Proportion
Ratio and Proportion: lesson, then the certificate test
Step 1: the lesson (about 1 min)
A ratio a : b compares two amounts; multiplying both terms by the same number does not change it.
- To split a total T in the ratio a : b, the shares are T × a ÷ (a + b) and T × b ÷ (a + b).
- If a : b = c : d (a proportion), then a × d = b × c.
- To join A : B and B : C, make the B terms equal first.
Worked example
Split ₹1,200 in the ratio 3 : 5.
- 3 + 5 = 8 parts
- One part = 1,200 ÷ 8 = 150
- Shares: 3 × 150 = 450 and 5 × 150 = 750
Answer: ₹450 and ₹750
Watch out
- A : B = 2 : 3 and B : C = 4 : 5 give A : B : C = 8 : 12 : 15, not 2 : 3 : 5.
Made by Shishya (AI-assisted): a general method in our own words, with our own example; no exam or platform question is copied.
Step 2: the test
- 15 questions from Shishya's checked question bank, 20 minutes. Pass mark: 11 correct.
- Scored on Shishya's server; the answers are not shown afterwards, so the test stays fair. Each attempt draws new questions.
- Free. Your first test needs no account; sign up free to take more. Your answers and score are not stored; if you pass, you choose the name to print (ages 13 and up).
- It is a Shishya completion certificate — not a university or government credential. The test is not supervised.