Book-2 Percents and Ratios
Ratios: Method 1: Cross multiply Method 2: Unknown Multiplier 1. In a class, the ratio of boys to girls is 5:8. If there are 40 gals, how many boys are there? 2. In a class, the ratio of boys to girls is 3:7. If there are 32 more gals than boys, how many boys are there? 3. Cement is crated using a 1:2:3 ratio of cement:sand:gravel. If we have 150 kg of sand, how many kg of concrete can be made? 4. On a high school team, the ratio of Sophomores to Juniors is 2:3, and ratio of Juniors to seniors is 5:6. Sophomores are what fraction of the whole team? 5. One cup of butter is enough for 12 cookies, and one cup of sugar is enough for 8 of her cookies. If there are 5 more cup of sugar than butter, How many cookies did she make? 6. 1. A jewel necklace contains only emeralds, rubies, and diamonds. If the ratio of emeralds to diamonds is 2:7 and the ratio of diamonds to rubies is 3:2, then which of the following could not be the number of jewels on the necklace? (A) 41B) 81(C) 82(D) 123(E) 205 7. 2. A tiara is studded with a mixture of gems. The ratio of sapphires to emeralds is 3:1. If 6 emeralds are added, the tiara will contain an equal number of sapphires and emeralds. How many emeralds must be added to the original tiara so that the ratio between emeralds and sapphires is 3:1? (A) 9(B) 12(C) 18(D) 24(E) 27 8. 3. An imperial scepter is mounted with diamonds, rubies, emeralds, and sapphires in the ratio of w : x : y : z. If w, x, y, and z are distinct single digit primes, then how many gems could be on the imperial scepter if it only contains the gems listed above? (A) 19(B) 58(C) 85(D) 97(E) Cannot be determined from the information provided above. 9. 4. (Okay - enough with the jewels!) Marty has a coin collection, which consists of only New World and Old World coins, in a ratio of 3:1. Marty's friend Kyle swaps 28 of his Old World Coins for 28 of Martin's New World coins. If Marty now has as many Old World coins as he does New World coins, how many coins did Marty originally have in his collection? (A) 28(B) 84(C) 112(D) 130(E) 390 10. (Okay, back to jewel necklaces). Marty has a necklace that contains a total of 36 rhinestones, zirconium, and obsidian "gems." If the ratio of obsidian to zirconium is 2:5, then which of the following could not be the number of rhinestones in Marty's necklace? (A) 8(B) 12(C) 15(D) 22(E) 29
1. 25 boys 5/8 = x/40, 8x=200, x=25 2. 24 3/7 = b/b+32,3b+96 = 7b,4b=96, b = 96/4, b = 24 method 2: 7n-3n = 32, 4n = 32, n = 8, therefore 8*3 = 24 3. 450 1.75+2.75+3.75 = 75 + 150 + 225 = 450kg 4. 10/43 S:j -> 2:3 J:S = 5:6 2:3 5:6 -> 10:15 15:18 Therefore 10:15:18 -> 10/43 5.120 cookies 6. B 7. D 8. C 9. C 10. B Solution: First is hit and trial. Second method: For A) do 36 - 8 = 28, now 28 is divisible by 7, why 7? 2x + 5x = 28, x = 28/7 Similarly check the rest.
Percentage Increase and Decrease. - Two parts: Increase by certain percent and find the actual increase. - 30% increase means multiply by 1.30 - 30% decrease means multiply by .70 - increase from 80 to 84 cents. What is the percent increase? a) (4/80)* 100 = 5% b) 4/80 = x/100 = 80x=400, x=5% 1.Price increase from 60 to 102, what was the percent increase? 2. price decrease from 250 to 200. 3. The price of an item increased from 200 to 800. What was the percent increase? 4. IF the price of a $30 shirt decreased by 20%, what was the final price of the shirt? 5. Watch out for greater than terminology: What number is 150% greater than 60? 6. If y is decreased by 20% and then increase by 60% what is the new number, expressed in terms of y? 7. y is 50% of x% of x Quantity A: y Quantity B: x
1. 70% increase Solution: 60.x=102, x=102/60,x=1.70 2. 20% decrease Solution 250x=200,x= 4/5,x=.80 3. 300% Solution: 200x=800,x=800/200, x = 4,i e 400% now 400-100 = 300, since they are asking for an increase. 4. Ans: 6 Two methods a) (20 of 30) / 100 = 6 b)20/100 = x/30 , x=6 5. Ans 150 Solution: (250*60) / 100 = 150 6. Ans. 32y/25 or 1.28y 7. Ans D Hint pick x as 100 and then x as 200.
Sequential increases: 1. Initial cost 100, increase of 30%, then discount of 30% 2. Increase by 20% then by another 5% 3. Pick number strategy: A shirt that initially cost 'd' dollars was on sale for 20% off. If 's' represent the sale price of the shirt, 'd' is what percent of 's'.
1. Ans 91 Solution: 100*1.30*.70 = 100*130*70/ 10000 = 13*7 = 91 2. Solution original*1.20*1.05 3. 125% Hint pick number 100. After discount 's' is 80. Therefore (100/80) * 100 = 125
Other questions: 1. If X>0, which of the following expressions are equal to 3.6% of 5x/12. Select all such expressions: A)3% of 20x B) x% of 3/2 C)3x% of 0.2 D) .05% of 3X E) 3x/200 2. Tuk weighs 60% more than Kim. Lee weighs 50% less than Tuk. Pat weighs 25% more than Lee. If Pat is 126, what is Kim's weight?
1. B and E 2. 126
Number sense technique: - Benchmark values: - 10%, 5%, 1% 1. 240 is 30% of what number? 2. 56 is what percent of 800? 3. What is 55% of 400? 4. What is 37% of 700? Practice problems: 1. What is 70% of 50 2. 48 is 30% of what number? 3. 72 is what percent of 300? 4. What is 35% of 180? 5. 90 is 15% of what number?
1. if 240 is 30% then divide 240/3 = 80, 80 is 10%, Therefore 100% is 800. 2. 80 is 10%, 8 is 1% then 8%7 = 56 and 1*7 = 7%, Therefore 56 is 7% of 800. 3. 10% is 40, 5% is 20, now 5%*11 = 55 and 20%11 = 220. Therefore 55% of 400 is 220. 4. 10% is 70, 1% is 7, 7% is 49. Now 210 + 49 = 259