Ratio and Proportion Questions for SSC CHSL

What is a Ratio

A ratio compares two quantities of the same kind. If A is 30 and B is 20, the ratio A:B = 30:20 = 3:2. Always simplify by dividing both numbers by their HCF. Ratios have no units. You can think of ratio as a recipe: 3 parts flour to 2 parts sugar — the actual amounts do not matter, only the proportion between them. Important: a:b and b:a are different. The order matters. Also, multiplying or dividing both terms of a ratio by the same non-zero number does not change its value.

• Ratio a:b means a/b. Always reduce to lowest terms.
• Ratio has no units — both quantities must be in the same unit before forming a ratio.
• If a:b = 3:2, then a = 3k and b = 2k for some value k. This k-trick is the key to solving most problems.
• Duplicate ratio of a:b is a squared : b squared.
• Sub-duplicate ratio of a:b is root(a) : root(b).
• Reciprocal ratio of a:b is b:a.

Proportion and Its Types

Proportion says that two ratios are equal: a:b = c:d, written as a:b::c:d. Here a and d are called extremes, b and c are called means. The golden rule: Product of extremes = Product of means, that is a x d = b x c. This is the single most tested fact about proportion in SSC CHSL. Think of proportion as a seesaw — both sides must balance. If you know three of the four values, you can always find the fourth.

• a:b::c:d means a/b = c/d, so ad = bc always.
• Fourth proportional to a, b, c is x where a:b = c:x, so x = bc/a.
• Third proportional to a, b is x where a:b = b:x, so x = b squared / a.
• Mean proportional between a and b is root(ab) — the geometric mean.
• Continued proportion: a:b = b:c means b squared = ac.

Dividing a Quantity in a Given Ratio

This is the most common word problem type in SSC CHSL. A sum of money or a line segment is divided among two or three people in a given ratio. The method is always the same: add the parts to get the total number of shares, then find the value of one share, then multiply. For three people with ratio a:b:c, total parts = a+b+c. First person gets (a / a+b+c) of the total.

• Sum of ratio parts is your denominator. Each person's fraction = their part / total parts.
• For ratio a:b:c, shares are a/(a+b+c), b/(a+b+c), c/(a+b+c) of total.
• If ratio changes (e.g., A:B = 2:3 changes to 3:4), re-solve with new ratio — do not mix old and new.

Comparing Ratios and Increasing/Decreasing Ratios

SSC CHSL sometimes asks which ratio is greater or asks you to find how much to add/subtract from numerator or denominator to change a ratio. Convert ratios to fractions and cross-multiply to compare. To increase a ratio, add to the numerator. To decrease, add to the denominator.

• To compare a:b and c:d, check if a x d is greater or less than b x c.
• If numerator increases more than denominator, the ratio increases.
• Adding same number to both numerator and denominator moves ratio toward 1:1.
• These problems often appear as: 'What must be added to both terms of 3:5 to make it 5:7?'

• Not converting units before forming a ratio — e.g., comparing 50 paise and Rs 2 directly as 50:2 instead of 50:200.
• Confusing third proportional with mean proportional — third proportional to a,b is b squared/a, not root(ab).
• In division problems, using the ratio number directly as the share instead of calculating the fraction of total — e.g., saying A gets 3 out of 3:5 total instead of 3/8 of the total.
• Forgetting that compound ratio is multiplication of ratios, not addition — 2:3 and 4:5 gives 8:15, not 6:8.
• When ratio involves three people and only two ratios are given (A:B and B:C separately), not equalising the B term before combining — this is a very common trap question.

• MEAN = Multiply Ends And kNow the middle — Mean proportional of a and b = root(a x b), because it sits between them geometrically.
• For FOURTH proportional, remember FM radio: Fourth = (b x c) / a. Forget a, multiply the middle two.
• k-trick mantra: Whenever you see a ratio, write a = mk and b = nk. Then use the condition given to find k. This one habit solves 80 percent of ratio word problems.
• Extremes and Means seesaw: a:b::c:d — outer ones (a,d) x each other = inner ones (b,c) x each other. Like a seesaw, outer weight = inner weight.

• SSC CHSL typically asks 2-3 questions on ratio per paper: one straightforward division problem, one on fourth or mean proportional, and one trickier word problem (age, salary, or mixture).
• Mean proportional and third proportional questions are almost always direct formula application — memorise the formulas and you get the mark in under 30 seconds.
• The 'what to add to both terms' question type appears regularly — practice the cross-multiplication shortcut instead of trial and error to save time.
• When A:B and B:C are given separately, make B equal in both ratios by finding LCM of B values before combining into A:B:C. This appears as a medium-difficulty question.
• Time target: Easy ratio questions in 30-45 seconds, word problems in 60-90 seconds. If a question takes longer than 2 minutes, skip and return — never get stuck on ratio problems as easier questions may be ahead.