Problems Related to Simplifications.

Problems Based on Simplifications.

1. David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?

A 19 B. 28 C. 30 D. 37

Answer: Option C

Explanation:

Suppose their paths cross after x minutes.

Then, 11 + 57x = 51 - 63x        120x = 40

x =	1
	3

Number of floors covered by David in (1/3) min. =		1	x 57		= 19.
		3

So, their paths cross at (11 +19) i.e., 30^th floor.

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Question 2:

(469 + 174)2 - (469 - 174)2 = ? (469 x 174)

A. 2 B. 4 C. 295 D. 643 Answer: Option B Explanation: Given exp. = (a + b)2 - (a - b)2 ab    = 4ab ab    = 4 (where a = 469, b = 174.) _________________________________________________________________________________ Question 3: A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be: A. 22 B. 23 C. 24 D. 26 Answer: Option D Explanation: Let the number of hens be x and the number of cows be y. Then, x + y = 48 .... (i)   and 2x + 4y = 140      x + 2y = 70 .... (ii) Solving (i) and (ii) we get: x = 26, y = 22.  The required answer = 26. __________________________________________________________________________________ Question 4: Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed ? A. 256 B. 432 C. 512 D. 640 E. None of these Answer: Option C Explanation: Let total number of children be x. Then, x x 1 x = x x 16     x = 64. 8 2  Number of notebooks = 1 x2 = 1 x 64 x 64 = 512. 8 8 __________________________________________________________________________________ Question 5: In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ? A. 160 B. 175 C. 180 D. 195 Answer: Option B Explanation: Suppose the man works overtime for x hours. Now, working hours in 4 weeks = (5 x 8 x 4) = 160.  160 x 2.40 + x x 3.20 = 432  3.20x = 432 - 384 = 48  x = 15. Hence, total hours of work = (160 + 15) = 175.