Question

Two numbers are respectively 20 percent and 50 percent more than a third number. What percent is the second of the first?​

Answer 1

I’ll present two approaches to solving this problem: an algebraic approach and and an applied approach. Let’s start with the applied approach.

We’ll call are through numbers A, B, and C. A is 20% more than C and B is 20% more than C.

Let’s pick an arbitrary number for C. Let’s say C is 100.

If C is 100, then A is 120 and B is 150. We know this because

A = C + 20% of C = 120% of C = 1.2C

and because C is 100, 1.2C is 120. The same logic applies for B being 150.

To figure out what percentage the first number (A) is of the second (B), it’s a simple fraction, A/B, converted to a decimal by dividing.

120/150 = 0.8, which, when expressed as a percentage, is 80%.

You can try this with any C. Let’s use 15 to see if we get the same answer.

C = 30

A = 1.2 * C = 36

B = 1.5 * C = 45

A / B = 36/45 = 0.8, or 80%

It works even when the numbers are decimals!

C = 18

A = 1.2 * C = 21.6

B = 1.5 * C = 27

A / B = 21.6 / 27 = 0.8, or 80%

So, practically, it appears that, for any chosen C, A is always 80% of B. Let’s see if we can make that into an equation so as not to rely on a few examples.

We know that A is always 1.2 * C. I’ll write that as 1.2C

We know that B is always 1.2 * C, which I’ll write as 1.5C

As above, to figure out what percentage A is of B, we make it into a fraction.

A / B = 1.2C / 1.5C

Now, there’s a C on the top AND bottom of our fraction, so we can cancel them out. We’re left with this:

A / B = 1.2 / 1.5 = 0.8, or 80%

Hope it helps :)