Problems on Simplification

Q1.	In a classroom, if 6 students per bench are assigned to accommodate all students, one more bench will be required. However, if 7 students are accommodate per bench, there would be a space left for 5 students.What is the number of students in the class ?
	30 45 42 72
	Answer: Option D Solution: Let the number of benches in the class be x. Then, 6(x + 1) = 7x - 5 x = 11. Hence, number of students in the class = 6 ( x + 1) = 6 x 12 = 72.
	Wrong Answer

Q2.	If a - b = 3 and a2 + b2 = 29, find the value of ab.
	10 12 15 18
	Answer: Option A Solution: 2ab = (a2 + b2) - (a - b)2    = 29 - 9 = 20 => ab = 10.
	Wrong Answer

Q3.	The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is
	Rs. 3500 Rs. 3750 Rs. 3840 Rs. 3900
	Answer: Option D Solution: Let the cost of a chair and that of a table be Rs. x and Rs. y respectively. Then, 10x = 4y   or   y = 5 x. 2 .'.  15x + 2y = 4000 =>  15x + 2 x 5 x = 4000 2 =>  20x = 4000 .'.  x = 200. So, y = ( 5 x 200 ) = 500. 2 Hence, the cost of 12 chairs and 3 tables = 12x + 3y     = Rs. (2400 + 1500)     = Rs. 3900.
	Wrong Answer

Q4.	5.8 ×2.5 + 0.6 ×6.75 + 139.25= ?
	157.30 157.80 158.40 None
	Answer: Option B Solution: Given exp. = 14.5 + 4.05 + 139.25 = 157.80.
	Wrong Answer

Q5.	On a sports day, if 30 children were made to stand in a column, then 16 columns could be formed. If 24 children were to stand in a column, then how many columns could be formed?
	20 22 29 30
	Answer: Option A Solution: Total number of children = (30 x 16) = 480. Number of columns of 24 children each = (480 /24) =20.
	Wrong Answer

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