This seems like a calculation intensive problem

Let us assume his savings = 2x

He invests x amount in a bond that pays simple interest for 2 years

Let us represent r% = R
550 = x*r%*2 ------1
275 = x*R

He invests the other half in a bond that pays compound interest for 2 years at the same rate

A = x*(1+R)^2 -------2
A-x = 605 --------3

Substitute 1 in 2 and in 3

A = 275/R*(1+R)^2 -----4
A - 275/R = 605 ------5

AR = 275*(1+2R+R^2) ------6
AR - 275 = 605R ------7

Substitute the value of AR from equation 7 in equation 6
275+605R = 275*(1+2R+R^2)
Simplifying

R(5R-1) = 0
R=0 or R=1/5 or r% = 1/5. Substitute this value in equation 1

275 = x*1/5 or x = 1375. Our original savings were 2x or 2750

I doubt the source. Is it a valid GMAT question?

Previous answer post is good in fact, but lets understand concept and then we can derive formula quickly

let 2T be the total savings before invested
and R be the Interest rate

First Understand concept of simple and compound interest

Simple Interest will be levied only on the capital invested so, SI = T*R*2 (Amount * Interest * Period)
2TR = 550
TR = 275

Compound Interest will be levied on capital + interest on previous period , CI = T*R+(T+T*R)R (Only 2 Periods considered here Interest for first year+ Interest for second year)

TR+(TR+T)R = 605
TR+TR+TR*R = 605
2TR+TR*R = 605
550+275R = 605
R=55/275 = 1/5

We know that TR = 275
T= 275*5 = 1375
But we need 2T = 2750

Cheers,
svd