Problem and Solution: Part 5 (Ratio Exercise problem and solution, Proportion Exercise problem and solution, Rate & Partnership Exercise problem and solution) ~ Explore Your Knowledge

Question: 27 Coffee A normally costs $ 100 per 1b. It is mixed with coffee B, which normally cost $ 70 per 1b, to form a mixture that costs $ 88 per 1b. If there are 10 1bs of the mix, how many pounds of coffee A is used in the mixture?
Option: (a) 4 (b) 5 (c) 6 (d) 7 (e) None

Explore: Let, a be the amount of coffee A present in per 1b of the mixture.
:. a x 100 + (1 - a)70 = 88
:. (100 - 70)a + 70 = 88
:. 30a = 18
:. a = 18/30 = 0.6 1b
:. In 10 1b, we have 6 1b of coffee A
Answer: (c)

Question: 28 Two blends of tea costing $ 2.80 and $ 3.20 per kg, respectively, are mixed in the proportion 2:3. The mixture is sold at $ 4.80 per kg, What is the percentage of profit?
Option: (a) 50.7 (b) 50.9 (c) 57.9 (d) 60

Explore: Let, tea of 1st kind and 2nd kind are mixed 2 kg & 3 kg, respectively.
:. Total cost of 5 kg mixtrue
= 2.8 x 2 + 3.2 x 3
= 5.6 + 9.6
=$ 15.2
Selling price of 5 kg = $ 4.8 x 5 = $ 24.0
:. Profit = $ 24 - $ 15.2 = $ 8.8
:. Percentage of profit
= {(Profit)/(Original cost)} x 100%
= {(8.8)/(15.2)} x 100%
= 57.9 %
Answer: (c)

Question: 29 Mr. John won an election where the ratio of his votes and those of his opponent, Mr. yunus was 4:3. The total number of voters was 581, of which 91 did not vote. Calculate the margin of votes by which Mr, Yunus was defeated.

Explore: No. of voters who applied their votes = 581 - 91 = 490
Ratio of votes of Mr. John & Mr. Yunus = 4:3
Sum of the ratio = 4 + 3 = 7
:. Mr. John got = 490 x (4/7) = 280
Mr. Yunus got = 490 x (3/7) = 210
:. Margin of votes = 280 - 210 = 70
Answer: The margin of votes by which Mr, Yunus was defeated was 70.

Question: 30 A sum of money is distributed among A, B & C. The amount of money received by A & B were in the ratio 1:2. The amount of money received by B & C were in the ratio 3:4. How much money did A receive?
Option: (a) 989 (b) 999 (c) 968 (d) 990 (e) None

Explore: 5 + 7 + 10 = 22. So, the number must he divisible by 22, 968 & 990 are both divisible by 22. But since we are looking for the largest value, 990 is the answer.
Answer: (d)

Question: 31 $1105 was divided between A, B & C. The amount of money received by A & B were in the ratio 1:2. The amount of money received by B & C were in the ratio 3:4. How much money did A receive?
Option: (a) $ 205 (b) $ 195 (c) $ 1500 (d) $ 100 (e) None of these

Explore: A:B = 1:2 = 3:6
B:C = 3:4 = 6:8
:. A:B:C = 3:6:8
:. A got {(3)/(3+6+8)} x 1105 = (3/17) x 1105 = $ 195
Answer: (b)
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