Ratio, Proportion, Partnership & Ages
🔒 Log in to trackRatio technique with its three biggest exam containers: proportion (mean/third/fourth proportional), partnership (capital × time profit splits) and ages (present vs shifted ratios). Tier 1 reliably has 2 questions from this cluster; most are 30–45 second marks once the multiplier habit is built.
One page per subtopic: detailed notes, every question type, formulas, tricks and practice sets.
Every formula on one printable page, grouped by subtopic.
5 exam-level questions worked step by step.
63 questions — untimed practice or a timed test with analysis.
Track record in the exam
Questions per shift in recent SSC CGL papers.
Test difficulty mix (63 questions)
Question patterns exams keep repeating
Taken from previous-year papers. If a pattern is marked "very common", expect to see it in your exam.
Share money in a ratio
very common"₹2,500 is divided among A, B and C in the ratio 2 : 3 : 5."
Add the ratio numbers to get the total parts.
Find one part, then multiply.
₹2,500 is divided among A, B and C in the ratio 2 : 3 : 5. Largest share?
Total parts = 2 + 3 + 5 = 10
1 part = 2500 ÷ 10 = 250
Largest = 5 parts = 5 × 250 = ₹1,250
Join two ratios into one
very common"A : B = 2 : 5 and B : C = 6 : 7. Find A : B : C."
Make the common letter the same number in both ratios.
Then write all three together.
If A : B = 2 : 5 and B : C = 6 : 7, find A : B : C.
B is 5 in one ratio and 6 in the other; make both 30
A : B = 2 : 5 = 12 : 30 (× 6)
B : C = 6 : 7 = 30 : 35 (× 5)
A : B : C = 12 : 30 : 35
Third, fourth and mean proportional
common"Find the third proportional to 12 and 18."
Write the proportion with an unknown x.
Cross-multiply and divide.
Find the third proportional to 12 and 18.
Third proportional means 12 : 18 = 18 : x
12 × x = 18 × 18 = 324
x = 324 ÷ 12 = 27
Share profit between partners
very common"A invests ₹30,000 for 12 months and B ₹40,000 for 6 months. Find A's share of the profit."
Multiply each person's money by the months it stayed.
Share the profit in that ratio.
A invests ₹30,000 for 12 months, B invests ₹40,000 for 6 months. Profit is ₹28,800. A's share?
A: 30,000 × 12 = 360,000
B: 40,000 × 6 = 240,000
Ratio = 3 : 2
A's share = 3/5 × 28,800 = ₹17,280
Ages in a ratio
very common"Present ages are in the ratio 4 : 5. After 16 years it is 6 : 7."
Write the ages as 4x and 5x.
Add (or subtract) the years to both, then cross-multiply.
Ages are in the ratio 4 : 5. After 16 years the ratio is 6 : 7. Sum of present ages?
Ages = 4x and 5x
After 16 years: (4x + 16) : (5x + 16) = 6 : 7
Cross-multiply: 28x + 112 = 30x + 96, so x = 8
Ages are 32 and 40, sum = 72 years
Income, spending and savings in a ratio
common"Incomes are 8 : 5, spendings 5 : 3, and each saves ₹1,200."
Write income and spending with separate letters (x and y).
Savings = income − spending, and both savings are equal.
Incomes of A and B are 8 : 5, spendings are 5 : 3, and each saves ₹1,200. Find A's income.
Incomes 8x and 5x, spendings 5y and 3y
Equal savings: 8x − 5y = 5x − 3y, so 3x = 2y, y = 1.5x
A saves 8x − 7.5x = 0.5x = 1200, so x = 2400
A's income = 8 × 2400 = ₹19,200
Coins in a ratio
occasional"Coins of 50 paise, 25 paise and 10 paise are in the ratio 7 : 6 : 5 with total ₹550."
Find the value of one set of coins (7 + 6 + 5 coins).
Divide the total by it to get the number of sets.
50p, 25p and 10p coins are in the ratio 7 : 6 : 5 and total ₹550. How many 25p coins?
One set: 7×50 + 6×25 + 5×10 = 550 paise
Total = ₹550 = 55,000 paise
Sets = 55,000 ÷ 550 = 100
25p coins = 6 × 100 = 600
Ratio of (x + y) to (x − y)
occasional"If (x + y) : (x − y) = 5 : 3, find x : y."
Give the two sides a common multiplier k.
Add them to get x, subtract them to get y.
If (x + y) : (x − y) = 5 : 3, find x : y.
Let x + y = 5k and x − y = 3k
Add: 2x = 8k. Subtract: 2y = 2k
x : y = 8 : 2
x : y = 4 : 1