Problem and Solution: Part 4 (Ratio Exercise problem and solution, Proportion Exercise problem and solution, Rate & Partnership Exercise problem and solution)

Question: 22 The ratio of gold and silver in an ornament weighing 42 gm is 4:3. How much gold will need to be added for the ratio of gold and silver to be 5:3?
Explore: The ratio of gold & silver = 4:3
Sum of the ratio = 4+3 = 7
The amount of gold = 42 gm x 4/7 = 24 gm
The amount of silver = 42 gm x 3/7 = 18 gm
Let, X gm gold will need to be added.
According to the question,
(24 +X ): 18 = 5:3
=> (24+X)/18 = 5/3
=> 72 + 3X = 90
=> 3X = 90 - 72 = 18
=> X = 18/3 = 6
Answer: 6 gm gold will need to be added

Question: 23 The ratio of boys and girls in a class is 1:2 and the classroom has 24 students. How many boys would have to be admitted to make ratio of boys to girls 1:1?

Option: (a) 6 (b) 8 (c) 10 (d) 12 (e) 14 Explore: Total no. of students = 24 Boys: Girls = 1:2 Sum of the ratio = 1+2 = 3 No. of boys = 24 x 1/3 = 8 No. of girls = 24 x 2/3 = 16 Let, X boys have to be admitted. According to the question, (8+X): 16 = 1:1 => (8+X) / 16 = 1/1 =1 => 8+X = 16 => X = 16 - 8 => X = 8 Answer: (b)

Question: 24 A jar contains white, red & green marbles in the ratio 2:3:4. Five more green marbles are added to make the ratio 2:3:5. How many white marbles are there in the jar?
Option: (a) 4 (b) 6 (c) 8 (d) 10 (e) None

Explore: Initially, white: green = 2:4
Let, G be the number of green marbles.
So, (White)/(Green) = 2/4 => (White)/G = 2/4
:. White = G/2
So, after 5 green marbles are added,
(White)/(Green) = (G/2)/(G + 5)
According to the problem,
(G/2)/(G + 5)
According to the problem,
(G/2)/(G + 5) = 2/5
=> (G)/(G+5) = 4/5 => 5G = 4G + 20
=> G = 20
:. No. of white marbles = 10
Answer: (d)

Question: 25 In an MBA class the ratio of number of commerce graduates to the number of science graduates is 2 to 5. If 2 more commerce graduates enter the class the ratio become 1 to 2. How many commerce graduates are in the class?

Explore: Let, there are 2X commerce graduates in the class and 5X science graduates.
According to the question,
(2X +2): 5X = 1:2
=> (2X+2)/5X = 1/2
=> 4X + 4 = 5X
=> 5X - 4X = 4
=> X = 4
Answer: No. of commerce graduates is 2 x 4 = 8

Question: 26 2 partners X & Y have 60% & 40% shares in business. After sometime a 3rd partner Z joined the business by investing $ 5 Lack & thus having 20% of the share in the business. What is Y's share now in the business?
Option: (a) 32% (b) 48% (c) 36% (d) 50% (e) None

Explore: Let, $X,Y,Z be X's, Y's & Z's share.
:. X/Y = 60/40 = 3/2
:. X = Y(3/2)
After Z joined the business we have
(X+Y)/Z = 80/20 [Z holds 20%, X & Y 80%]
:. ((5/2)Y)/500000 = 4 => (5/2)Y = 20,00,000
:. Y = 8,00,000
:. X = (3/2)Y = (3/2) x 8,00,000 = 12,00,000
:. X:Y:Z = 12,00,000 : 8,00,000 : 5,00,000
= 12 : 8 : 5
:. Y's share = 8/(12+8+5) x 100%
= 8/25 x 100%
= 32%
Answer: (a)

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