Question

Q 100. A number N is divided into three parts such that
sum of first 2 parts is equal to K% of 3rd part.
What is the 3rd part?​

Answer 1

Step-by-step explanation:

the first part = p1; the second part = p2 and the third part = p3 then

N = p1+p2+p3

N-p3 = p1+p2

p1+p2 = p3 * K * 0.01* N

p3 * K * 0.01* N = p1 + p2

p3 * 0.01 * K * N = p1 + p2

p3 = (p1 + p2) / 0.01* K * N

p3 = (p1+p2) / (0.01 * K * N)

p3 = 100 * (p1+p2) / (K*N)

I checked this equation where

K = 25% ; p3 = 300 while (p1 + p2) = 900 and N = 1200 and found it to tally.

Answer 2

Let X, Y and Z be three parts

X + Y = k x Z/ 100
100( X + Y ) = k Z
100 ( N - Z) = kZ
100 N = (100+k)Z
Z = 100 N/ (100+K)


Z percentage = Z / N x 100 %
= 100 N / N x 100/ (100+k) %
= 10,000/ ( 100 + k) %

So if k= 25%
Z % = 10,000/125 = 80%

Z = 100/125N = 0.8 N