correct answer: b) 750 & 250

Explanation

Let, Smaller number is ‘x’
Greater number is ‘y’
According to the question,
\left(x+y\right)=1000
\rightarrow x=1000-y ----(1)
And, 3x=y
\rightarrow x=\frac{y}{3} ----(2)
So, from (1) & (2) we get,
1000-y=\frac{y}{3}
\rightarrow3\left(1000-y\right)=y _{[cross multiply]}
\rightarrow3000-3y=y
\rightarrow-3y-y=-3000
\rightarrow-4y=-3000
\rightarrow y=\large\frac{-3000}{-4}
\rightarrow y=750
Put the value in no (1) equation, we get:
x=1000-750
\rightarrow x=250
\therefore Greater number is 750 and smaller number is 250 .
Ans: The numbers are 750 & 250.

An alternative way to phrase this particular query is possible:
1. Calculate the numbers if their total is 1000 and the larger number is three times the smaller one.
2. What are the two numbers if their sum is 1000, with one number being three times the other?
3. Find out the values of the two numbers when one is three times the other and their sum is 1000.