Friday, November 22, 2013

Problem and Solution: Part 3 (Ratio, Proportion, Rate & Partnership)

Question: 17 If Marie has twice as much money as Curie has, who has three times as much money as Sunny has. What is the ratio of the amount of money Sunny has to the amount of money Marie has?
Option: (a) 1:8 (b) 1:6 (c) 1:4 (d) 1:2 (e) 2:1

Explore : Let, Sunny hat $ X
:. Curie has $ 3X
:. Marie has $ (3X x 2) or $ 6X
:. The ratio of amount of money Sunny has to the amount of money Marie has
= X:6X = X/6X = 1/6 = 1:6
Answer: (b)

Question: 18Masum has twice as much money as Selim and Selim has 50% more money than what Babal has. If the average money with them is $ 110, then determine the amount of Masum's Money.
Explore: Let, Babal has $ X
:. Selim has $ (X + X x 50%)
= $ (X x 0.5%X)
= $1.5X
:. Masum has $ (1.5X x 2) = $3X
According to the question,
     X + 1.5X + 3X = 110 x 3
=> 5.5X = 330
=> X = 3.30/5.5 = 60
:. Masum has $ (3 x 60) = $ 180
Answer: $ 180

Question: 19 The cost of a book is 1.5 times that of a CD. The price of a pencil is 1/3 rd of that of a pen, The cost of the pen is twice as much as that of the CD. What is the ratio of cost of the book to cost of the pencil?
Explore: Let, the cost of CD =X
:. Cost of a book = 1.5X
Cost of a pen = 2X
?Cost of a pencil = 2X x 1/3 = 2X/3
:. The ratio of cost of the book to the cost of the pencil
= 1.5X :2X/3 = 1.5X/(2X/3) = 1.5X x 3/2X
= 4.5/2 = 9/4 = 9:4
Answer: 9 : 4

Question: 20 A room has a floor area of 150sq. feet. If the length & breath of the room are in the ratio 3:2, then what is the length of the floor in feet?
Option: (a) 10 (b) 15 (c) 20 (d) 9 (e) None

Explore: Let, L be the length of the room
According to the problem,
length/ width = 3/2
Or, L/width = 3/2 => width 2L/3
:. L x 2L/3 = 150
=> LxL = (3 x 150)/2 = 3 x 3 x 25
:. L 3 x 5 = 15
Answer: (b)

Question: 21 A gentleman spends 2/5th of his monthly income on food, 1/4th on education and the rest $ 200 is saved. What is his monthly income?
Option: (a) 2000 (b) 1500 (c) 1200 (d) 1000 (e) None

Explore: Let, X be his monthly income.
:. (2/5)X  + (1/4)X + 200 = X
:. 200 = X - (2/5)X - (1/4)X
= X (1-2/5 -1/4)
= X((20-8-5)/20) = X(7/.20)
:. X = (200 x 20)/7 571.43
Answer: (e)

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