If $d$ is $10/%$ greater than $c,$ $c$ is $25/%$ less than $b,$ and $a$ is $50/%$ greater than $b,$ by what percent is $d$ less than $a?$

Answer: d is 45% smaller than a.

Step-by-step explanation:

Here we have:

d = (1 + 0.10) * c = 1.10*c

c = (1 - 0.25) * b = 0.75*b

a = (1 + 0.5) * b = 1.5*b

we want to find the relation between a and d.

we can replace the second equation into the first one:

d = 1.10*c = 1.10 * (0.75*b) = 0.825*b

then b = d/0.825 = d*1.21

Now we can replace it into the third equation:

a = 1.5*b = 1.5 * (1.21*d) = 1.815*d

a * (1/1.815) = d

a*0.55 = d

a * (1 - 0.45) = d

This means that d is 45% smaller than a.