Fractions and Percentages

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.

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

Lac has 68-90% resin.

'Lead pencils' contain no actual lead metal. They are made of graphite (a form of carbon) mixed with clay. The name originated historically when graphite was mistaken for a form of lead. Graphite is still sometimes called 'black lead' in certain contexts, but modern pencils contain 0% lead.

Steel is an alloy primarily composed of iron and carbon. The carbon content typically ranges from 0.1% to 1.5% for most common steels - mild steel has 0.05-0.25%, medium carbon steel 0.25-0.60%, and high carbon steel 0.60-1.0%. This range covers the vast majority of commercial steel applications. Options B, C, and D represent carbon levels that would approach cast iron or exceed typical steel compositions.

As per the given data: X = Z * (80/100) => X is 20% less than Z. Y = Z * (72/100) => Y is 28% less than Z. Lets assume Y is m% less than X. So, Y = X(100 - m)/100 => z * (72/100) = Z * (80/100) (100 -m)/100 => m = 90 =>100 - m = 10 So, Y is 10 % less the number X. Option 5 is correct.