Fractions and Percentages

Steel is an alloy of iron and carbon, where carbon content typically ranges from 0.1% to 1.5%. This carbon content is crucial as it determines steel's hardness and strength - higher carbon makes steel harder but more brittle. Options B, C, and D suggest carbon percentages that are too high for standard steel; such compositions would result in cast iron (2-4% carbon) or unusable brittle material.

Lead pencils contain graphite (carbon), not actual lead metal. The name comes from historical confusion when graphite was thought to be a form of lead. Therefore, the percentage of lead is zero.

The maximum zoom percentage in excel is 400%. Hence, this option is an invalid zoom percentage.

Let the original fraction be n/p.

 (1.7*n)/(0.9*p) = 7/15

So, n/p = 21/85

Let the original fraction be n/p.

Then, according to question, (0.7 x n)/(0.6 x p) = 7/9

n/p = 6/9 = 2/3

Let the initial number be x. Percentage decrement = (x/3x) X 100 = (100/3)% = 33.33%

k = 8 (2/100) = 16/100 l = 10 (1/100) = 10/100  k + l = (16/100) + (10/100) = 26/100 = 0.26

Despite the name, 'lead pencils' contain zero percent lead. The core is actually made of graphite (a form of carbon) and clay. The misnomer dates back to the 16th century when graphite was mistaken for a form of lead. Modern pencils use graphite, not lead.

Given: a = (2/3)b, b = (2/3)c, c = (2/3)d. We need b as fraction of d. From c = (2/3)d, we get d = (3/2)c. From b = (2/3)c, we get b = (2/3)c. So b/d = (2/3)c / (3/2)c = (2/3) / (3/2) = (2/3) × (2/3) = 4/9. Therefore b is 4/9 of d.

x% of y = (x/100) × y = (x × y)/100. Similarly, y% of x = (y/100) × x = (x × y)/100. Since multiplication is commutative, these are equal. The algebraic structure is symmetric, making x the correct answer.

Given x/y = 4, x = 4y. We want (2x-y)/x as percentage. Substituting: (8y-y)/(4y) = 7y/4y = 7/4 = 1.75 = 175%.

We need b as fraction of d, so express b in terms of d. Given: b=2c/3, and c=2d/3, so b=2(2d/3)/3=4d/9. Therefore b is 4/9 of d. The key is substituting step by step until you reach the target variable.

Initially: 60 games played with 30% wins = 18 wins. Let x be consecutive wins needed. Total wins = 18 + x. Total games = 60 + x. We want (18+x)/(60+x) = 50% = 0.5. Solving: 18 + x = 0.5(60 + x) = 30 + 0.5x. So 0.5x = 12, and x = 24. The team needs to win 24 games in a row to reach 50% overall.

(90% - 85%)x = 225 5% of x = 225 x = (225 * 100)/5 = 4500 90% of 4500 = 4050