a) 765 & 235

b) 750 & 250

c) 728 & 272

d) 716 & 284

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.**