Directions : Read the following table carefully and answer the questions given…
2022
Directions : Read the following table carefully and answer the questions given below.
Table shows the percentage distribution of poems published out of total poems & stories published starting from 2011 to till 2013. Table also shows number of poems published starting from 2011 to till 2013.
Note: (a) Y+X=115
(b) Z=Y-X
(c) Y+Z=95
The ratio between number of stories published in 2012 to 2016 is (Y-3) : 3Z. If the number of stories published in 2016 is 40% of the total number of poems & stories together published in 2016, then number of poems published in 2011 is what percentage more than the number of poems published in 2016?
- A.
[41X – (25Y + 91)] %
- B.
Both [41X – (25Y + 91)]% and [Z/5 – 1]%
- C.
[0.12Y – 4] %
- D.
Both [41X – (25Y + 91)]% and [0.12Y – 4]%
- E.
[Z/5 – 1]%
Show answer & explanation
Correct answer: B
Concept
In a percentage-distribution table, if poems are P% of the combined poems-and-stories total, then Total = Poems ÷ (P/100) and Stories = Total − Poems. When a ratio links a known quantity to an unknown one, the unknown is found by scaling the known value with that ratio. Finally, 'A is what percent more than B' = (A − B)/B × 100.
Step 1 — Solve the three Note relations for X, Y, Z
Combine Y + X = 115 with Z = Y − X inside Y + Z = 95, giving 2Y − X = 95.
Replace X = 115 − Y: 2Y − (115 − Y) = 95 ⇒ 3Y = 210 ⇒ Y = 70.
Then X = 115 − Y = 45, and Z = Y − X = 25. (Check: 70 + 25 = 95 and 25 = 70 − 45.)
Step 2 — Poems published in 2012 (per-year)
The 'Number of poems published' column is cumulative ('Till 2012' = 1640, '2011' = 702), so poems published in 2012 alone = 1640 − 702 = 938.
Step 3 — Stories published in 2012
Poems in 2012 are Y% = 70% of that year's poems-and-stories total, so stories are the remaining 30%.
Total poems & stories in 2012 = 938 ÷ 0.70 = 1340.
Stories in 2012 = 1340 − 938 = 402.
Step 4 — Stories published in 2016 (use the given ratio)
Stories in 2012 : stories in 2016 = (Y − 3) : 3Z = (70 − 3) : (3 × 25) = 67 : 75.
Stories in 2016 = 402 × (75 ÷ 67) = 450.
Step 5 — Poems published in 2016
Stories in 2016 are 40% of that year's total, so poems are the remaining 60%.
Total in 2016 = 450 ÷ 0.40 = 1125.
Poems in 2016 = 1125 − 450 = 675. (Or directly: 450 is 40%, so 60% = 450 × 60/40 = 675.)
Step 6 — Required percentage
Poems in 2011 = 702; poems in 2016 = 675.
Percentage more = (702 − 675) ÷ 675 × 100 = 27 ÷ 675 × 100 = 4%.
Why two of the algebraic forms give the same value
The required 4% can be written purely in the variables, and two of the listed forms reduce to exactly 4 at X = 45, Y = 70, Z = 25:
41X − (25Y + 91) = 41×45 − (25×70 + 91) = 1845 − 1841 = 4.
Z/5 − 1 = 25/5 − 1 = 5 − 1 = 4.
By contrast, 0.12Y − 4 = 0.12×70 − 4 = 8.4 − 4 = 4.4, which is not 4.
Since exactly the two forms 41X − (25Y + 91) and Z/5 − 1 both equal the required 4%, the choice that names both of those forms together is the complete answer.