Directions : Read the following table carefully and answer the questions given…

Concept

In a percentage-based data table, when a category's count and its share of the whole are known, the whole is recovered by Whole = Part / (Percent/100), and the complementary category equals Whole minus the given part. Cumulative ('Till year') totals are converted to a single year by subtracting the previous cumulative value.

Step 1 - Solve the note constraints for X, Y, Z

1. Y + X = 115

2. Z = Y - X, so substituting into Y + Z = 95 gives 2Y - X = 95

3. Adding Y + X = 115 and 2Y - X = 95 gives 3Y = 210, hence Y = 70

4. Then X = 115 - 70 = 45 and Z = Y - X = 70 - 45 = 25

So X = 45, Y = 70, Z = 25.

Step 2 - Recover poems published in each single year

The 'Number of poems' column is cumulative, so the per-year poem counts are obtained by successive subtraction:

1. Poems in 2011 = 702

2. Poems in 2012 = 1640 - 702 = 938

3. Poems in 2013 = 1910 - 1640 = 270

Step 3 - Find stories using the percentage share of poems

For each year, poems are the given percent of that year's total (poems + stories), so total = poems / (percent/100) and stories = total - poems.

1. 2012: poems = 938 are Y% = 70% of the total, so total = 938 / 0.70 = 1340, and stories = 1340 - 938 = 402

2. 2013: poems = 270 are Z% = 25% of the total, so total = 270 / 0.25 = 1080, and stories = 1080 - 270 = 810

Step 4 - Required difference

Difference between stories in 2012 and 2013 = 810 - 402 = 408.

Cross-check with the option expressions

Evaluate each expression at X = 45, Y = 70, Z = 25:

• 9X + 15 = 9(45) + 15 = 420

• 6Y - 12 = 6(70) - 12 = 408

• 17Z - 12 = 17(25) - 12 = 413

Only 6Y - 12 equals the required difference of 408, so that is the answer.