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23 Oct 2019, 01:21
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
75% (02:21) correct
25%
(02:20)
wrong
based on 81
sessions
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A company was approved to spent a certain sum of money for an annual. It spent (1/4)th of the sum during the first quarter of the year, and (1/6)th of the remainder was spent during the second quarter. By what percent is the sum of money that was left at the beginning of the third quarter more than that spent in the last two quarters?
(A) 10%
(B) 22.22%
(C) 33.33%
(D) 66.66%
(E) 133.33%
(A) 10%
(B) 22.22%
(C) 33.33%
(D) 66.66%
(E) 133.33%
Updated on: 23 Oct 2019, 08:39
Originally posted by Archit3110 on 23 Oct 2019, 02:15.
Last edited by Archit3110 on 23 Oct 2019, 08:39, edited 2 times in total.
Last edited by Archit3110 on 23 Oct 2019, 08:39, edited 2 times in total.
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Bunuel
A company was approved to spent a certain sum of money for an annual. It spent (1/4)th of the sum during the first quarter of the year, and (1/6)th of the remainder was spent during the second quarter. By what percent is the sum of money that was left at the beginning of the third quarter more than that spent in the last two quarters?
(A) 10%
(B) 22.22%
(C) 33.33%
(D) 66.66%
(E) 133.33%
(A) 10%
(B) 22.22%
(C) 33.33%
(D) 66.66%
(E) 133.33%
1st ; x/4
2nd ; 3x/4 *1/6 ; x/8
total spent in 1st & 2nd ; 3x/8
for 3rd & 4th quarter we have ; x-(x/4+x/8) = 5x/8
total 1 &2 ; 3
%∆ ; 5x-3x/3x ; 2x/3x ; 66.66%
IMO D
23 Oct 2019, 05:37
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Solution
Given:
- • A company spent \((\frac{1}{4})^{th}\) of the sum during the first quarter of the year, and
• \((\frac{1}{6})^{th}\) of the remainder was spent during the second quarter
To find:
- • What percent is the sum of money that was left at the beginning of the third quarter more than that spent in the last two quarters
Approach and Working Out:
- • Let the amount be 100x
- o After 1st quarter, remaining amount = \(100x – \frac{100x}{4} = 75x\)
o After 2nd quarter, the remaining amount = \(75x – \frac{75x}{6} = 62.5x\)
• Amount remaining at the beginning of third quarter = 62.5x
• Amount spend in first two quarters = 100x – 62.5x = 37.5x
• Therefore, required percentage = \(\frac{(62.5 – 37.5)}{37.5} * 100 = 66.66%\)
Hence, the correct answer is Option D.
Answer: D
