
182 A.2d 432 (1962)
George BENOIT ex ux.
v.
ZONING BOARD OF REVIEW OF the CITY OF WOONSOCKET.
M. P. No. 1469.
Supreme Court of Rhode Island.
June 28, 1962.
*433 Irving I. Zimmerman, Woonsocket, for petitioners.
Janice A. Fournier, Asst. City Sol. for City of Woonsocket, for respondent.
PAOLINO, Justice.
This is a petition for certiorari to review a decision of the zoning board of review of the city of Woonsocket denying the petitioners' application for a variance. We issued the writ and pursuant thereto the pertinent records have been certified to this court.
It appears therefrom that petitioners own a small lot located at the corner of Park avenue and Transit street in a R-3 single-family and two-family residence district in which commercial uses are prohibited. The lot has an area of 1,192 square feet and contains a building measuring 35 by 20 feet. For over thirty years they operated a small neighborhood grocery store on the premises. After the enactment of the original zoning ordinance this use became a nonconforming use.
The petitioners used the premises as a grocery store until December 1960, after which time it was apparently vacant until the latter part of 1961. It appears from the record that on July 24, 1961 petitioner George Benoit and Rose A. Dumont, a prospective tenant, applied to the board for a variance for permission to use the building as a sewing and alteration shop. The board held a hearing thereon on August 15, 1961 and granted the application with the express proviso that the proposed use was to be limited to "self-employment by Rose A. Dumont, as applied for." No remonstrants appeared at that hearing and no appeal has been taken from the board's action on the July 24, 1961 application.
After the granting of that application petitioners divided the building into two parts. The entrance to the front portion was on Park avenue and the entrance to the rear portion was on Transit street. Their application to the building inspector for a permit to make the alterations necessary to divide the building was denied. Thereafter, on December 18, 1961, petitioners and Olive Gilmore joined in an application to the board for a variance to permit the use of the rear portion for a beauty salon.
The board held a hearing on this application on January 8, 1962. The petitioners admitted that the July 24, 1961 application contemplated only one business operation on the premises. The petitioner Blanche Benoit explained their reason for dividing the store as follows: "While the shelves and all the tables were in the store, the store looked very small. When they were all removed, it was now big. She [Rose A. Dumont] thought she didn't need all that space for the little business she has; she asked me to separate it so as not to heat the whole place,  it would be too much for her."
The petitioners are seeking a variance under G.L. 1956, § 45-24-19(c). They base their claim of hardship mainly on the ground that they are receiving only $15 per week for the front portion instead of the rent of $35 per week which Rose A. Dumont agreed to pay for the entire premises. The petitioner Blanche Benoit also *434 testified that the money they spent to renovate the building created a hardship. The application alleges that the building has always been used as a store and that it is completely unsuited for residential use.
After the hearing the board denied the application on the ground that no hardship had been proved. The petitioners contend that the board's decision was arbitrary, unreasonable and an abuse of discretion. They argue that since the board found hardship existed when it granted the July 24, 1961 application, it could not at a later time, without any change of circumstances as to the hardship, find that there was no hardship. In our opinion this argument is not pertinent to the facts in evidence.
In the posture in which this case is presented the narrow issue before us is whether the evidence supports the board's finding that no hardship has been proved and whether in making such finding the board applied the correct rule of law. The burden of proving unnecessary hardship is on petitioners. D'Acchioli v. Zoning Board of Review, 74 R.I. 327, 60 A.2d 707. The board expressly found that they have not sustained this burden of proof. On certiorari to review the decision of the board petitioners, as appellants, have the burden of persuading this court that the board has abused its discretion. Pistachio v. Zoning Board of Review, 88 R.I. 285. 147 A.2d 461.
After careful consideration it is our opinion that the decision of the board is supported by the evidence and that in finding no hardship the board applied the correct rule of law. The evidence indicates that the denial of the application merely deprives petitioners of the most profitable use of their premises. This is not sufficient in law to support a finding of unnecessary hardship. Strauss v. Zoning Board of Review, 72 R.I. 107, 48 A.2d 349. The evidence clearly would not support a finding that the denial of the variance would deprive the petitioners of all beneficial use of their property. In the circumstances, after carefully considering all of their contentions, it is our opinion that the petitioners have failed to sustain their burden of proving that the board's decision was arbitrary, unreasonable or an abuse of discretion.
The petition for certiorari is denied and dismissed, the writ heretofore issued is quashed, and the decision of the respondent board is affirmed. The records which have been certified to this court are ordered sent back to the respondent board.
