As per table, in the month of July, the votes of D and C are in the ratio 9 :…

Concept

A ratio fixes only the relative sizes of two quantities, so when one of them is held constant, demanding a particular ratio forces the other quantity to exactly one new value.

A percentage increase is always measured against the quantity’s own original value: increase % = (new value − original value) ÷ original value × 100.

Application

1. Read the July row of the table: D = 4.5 lakh and C = 2.5 lakh, so D : C = 4.5 : 2.5 = 9 : 5, exactly as the stem states.

2. D stays at 4.5 lakh while D : C is to become 5 : 9, which gives the equation 4.5 ÷ Cnew = 5 ÷ 9.

3. Cross-multiplying: 5 × Cnew = 4.5 × 9 = 40.5, so Cnew = 40.5 ÷ 5 = 8.1 lakh.

4. The rise C must undergo is 8.1 − 2.5 = 5.6 lakh.

5. Expressed against C’s own July value, that rise is (5.6 ÷ 2.5) × 100 = 224%.

Cross-check

• Substituting back: 2.5 × (1 + 224 ÷ 100) = 2.5 × 3.24 = 8.1 lakh, and 4.5 : 8.1 = 45 : 81 = 5 : 9, the ratio the question asks for.

• Ratio-scaling shortcut: with D held fixed, turning 9 : 5 into 5 : 9 multiplies C by (9 ÷ 5) ÷ (5 ÷ 9) = 81 ÷ 25 = 3.24, that is a rise of 3.24 − 1 = 2.24 times its own value, or 224%.

• A common slip is to divide the 5.6 lakh rise by D’s 4.5 lakh instead of by C’s own 2.5 lakh; the base of a percentage change must be the quantity that changes.

Hence C’s July votes must increase by 224%.