Paper 1 · Mathematical Reasoning and Aptitude
UGC NET December 2021 June 2022 (13.10.2022) Shift-I
Given below are two statements. Statement I: One-fourth of sixty percent of a number equals two-fifths of twenty percent of another number, and the ratio of the first number to the second is 8:15. Statement II: A student studies from 11:00 am to 8:00 pm on each of the five weekdays and one-third of that time on Saturday, taking Sunday off; the fractional part of the entire week that the student studies is 3/7. In the light of the above statements, choose the correct answer from the options given below.
- Statement I: One-fourth of sixty percent of a number equals two-fifths of twenty percent of another number, and the ratio is 8 to 15.
- Statement II: The student studies 9 hours on each of 5 weekdays and 3 hours on Saturday; the fraction of the whole week studied is 3/7.
ABoth Statement I and Statement II are true
BBoth Statement I and Statement II are false
CStatement I is true but Statement II is false ✓ Correct
DStatement I is false but Statement II is true
Correct answer: (C) Statement I is true but Statement II is false — The answer is that Statement I is true but Statement II is false.
Explanation
★The answer is that Statement I is true but Statement II is false.
★One-fourth of sixty percent is fifteen percent, and two-fifths of twenty percent is eight percent.
★Setting 15 percent of the first equal to 8 percent of the second gives a ratio of 8 to 15, so Statement I is true.
★The student studies 9 hours on each of 5 days and 3 hours on Saturday, totalling 48 hours.
★The week has 168 hours, and 48 over 168 is 2/7, not 3/7, so Statement II is false.
★Thus only the first statement holds.
★So the answer is that Statement I is true but Statement II is false.
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