Directions : Line chart given below shows expense of five persons (in %) out…
2018
Directions : Line chart given below shows expense of five persons (in %) out of total income of two months. Income of persons is same in both months.
‘B’ invested some amount of his saving in PPF account in November. Find the amount invested by ‘B’ in PPF account?
(I) Amount invested by ‘B’ in PPF is 62.5% less than amount expend by ‘B’ in April while difference between amount expend by ‘B’ in November and April is Rs. 16,000.
(II) ‘B’ invested 37.5% of his saving in PPF account while difference between saving of ‘B’ in November and April is Rs 16,000.
- A.
Statement (I) alone is sufficient to answer the question but statement (II) alone is not sufficient to answer the questions.
- B.
Statement (II) alone is sufficient to answer the question but statement (I) alone is not sufficient to answer the question.
- C.
Both the statements taken together are necessary to answer the questions, but neither of the statements alone is sufficient to answer the question.
- D.
Either statement (I) or statement (II) by itself is sufficient to answer the question.
- E.
Statements (I) and (II) taken together are not sufficient to answer the question.
Show answer & explanation
Correct answer: D
Concept
In a data-sufficiency item, each statement is judged independently for whether it pins down a single numerical answer. From the chart, B's monthly expense is a fixed percentage of income, and since income is identical in both months, saving = income - expense for each month. A statement is sufficient if it lets you solve for the income (the one unknown) and then compute the required PPF amount.
Reading the chart for B
November expense of B = 60% of income, so November saving = 40% of income.
April expense of B = 40% of income, so April saving = 60% of income.
Applying Statement (I)
Let B's monthly income be X. Difference between November and April expense = 60%X - 40%X = 20%X.
Given this difference is Rs 16,000: 0.20X = 16,000, so X = Rs 80,000.
April expense = 40% of 80,000 = Rs 32,000.
PPF is 62.5% less than April expense = 32,000 x (1 - 0.625) = 32,000 x 0.375 = Rs 12,000.
Statement (I) on its own fixes the income and yields a unique PPF amount.
Applying Statement (II)
Difference between November and April saving = 60%X - 40%X = 20%X.
Given this difference is Rs 16,000: 0.20X = 16,000, so X = Rs 80,000.
November saving = 40% of 80,000 = Rs 32,000.
PPF = 37.5% of November saving = 0.375 x 32,000 = Rs 12,000.
Statement (II) on its own also fixes the income and yields the same unique PPF amount.
Cross-check and conclusion
Both statements independently determine income as Rs 80,000 and both give PPF = Rs 12,000. Because each statement alone settles the question, either one by itself is sufficient.