Ratio and Proportion Basics

Ratio and proportion is the backbone of the SBI Clerk arithmetic block: ages, partnership, mixtures and many DI questions all reduce to a ratio step. A ratio a : b compares two quantities of the same unit, and a proportion says two ratios are equal. Because the concept feeds so many other topics, five to six marks across the paper hinge on handling ratios cleanly and fast.

Simplify Before You Solve

Always reduce a ratio to its lowest terms first by dividing both parts by their HCF, because a clean ratio like 3 : 4 is far easier to scale than 45 : 60. If a ratio has fractions, multiply every term by the LCM of the denominators to clear them; if it has decimals, multiply by a power of ten. This single habit removes most arithmetic slips and makes the next step — dividing a sum or comparing quantities — almost instant.

Combining Two or More Ratios

When A : B and B : C are given separately, make the common term B equal in both before joining them. If A : B = 2 : 3 and B : C = 4 : 5, scale the first to 8 : 12 and the second to 12 : 15 so B is 12 in each, giving A : B : C = 8 : 12 : 15. This bridging trick is the heart of most three-quantity ratio questions and appears constantly in age and partnership sums, so drill it until it is a reflex.

If A : B = a : b and B : C = c : d, then A : B : C = ac : bc : bd (scale so B matches)

Dividing a Sum in a Given Ratio

To split an amount in the ratio a : b : c, add the parts to get the total number of shares, then each person's amount is their part divided by the total shares, times the sum. For 6,600 split as 2 : 3 : 6, the total is 11 shares, so one share is 600 and the amounts are 1,200, 1,800 and 3,600. Think in terms of one share value and the rest follows in a single multiplication each — no long working, no repeated division, and almost no chance of a careless error.

Solved Examples

Example 1: Divide 7,200 among P, Q, R in 3 : 4 : 5. Total shares = 12, so one share = 600. Amounts are 1,800, 2,400 and 3,000 — read straight off one share value.

Example 2: If A : B = 2 : 3 and B : C = 6 : 7, then B is 3 and 6; take LCM 6, so A : B = 4 : 6, giving A : B : C = 4 : 6 : 7 in one step.

✗ Adding the ratio terms 2 : 3 and 4 : 5 directly to get 6 : 8  |  ✓ Equalising the common term B first, then merging to A : B : C

Reading What the Question Wants

A frequent trap is that the question asks not for a share but for a difference or a total of two shares, so read the final line carefully before you compute. If P and R together are asked from a 2 : 3 : 6 split, add their parts, 2 and 6, giving 8 of 11 shares. Equally common is a question that gives one person's actual amount and asks for another's, which you solve by finding one share value from the known amount and scaling. The arithmetic is easy; the only marks lost here come from answering a slightly different question than the one printed.