Whittemore, J.

The issue on these appeals from two decrees of the Superior Court is the validity of the judge’s *531 determination that the denials by the Brockton zoning board of appeals of variances to the plaintiffs should be annulled.

The plaintiffs 2 in the two suits are, respectively, owners of two parcels of land on the easterly side of North Quincy Street, a way which, according to Brockton city maps, is, where it abuts the plaintiffs’ parcels, entirely in Brockton. According to those maps, the Brockton-Abington boundary runs through the parcels of the plaintiffs so as to place in Brockton a narrow strip of land ranging in width along the two parcels from fourteen to twenty-three feet. The Brock-ton zoning ordinance places this strip in a residential zone. The greater part of each parcel is in Abington and is zoned and usable only for business. The only access to these parcels is from North Quincy Street. Under the Brockton zoning ordinance no structure can be built on the land of either plaintiff lying in Brockton as each area is too small for any type of residence.

The plaintiff Lapenas sought a variance under the Brock-ton ordinance for access to a gasoline station for which the building inspector of Abington had issued a permit. The plaintiff Thompson for years has had a market on her Abington land and now has a shopping center there. She seeks a variance to validate the existing use of her Brock-ton land for access to her Abington land.

The agreed facts state that the county commissioners relocated North Quincy Street in part in 1834, and the remainder in 1838, so that the easterly side of the highway was in Abington and the westerly side was in Brockton. It is agreed also that the Brockton city plans do not show North Quincy Street as thus relocated. In all deeds of record since before the adoption of the Brockton zoning ordinance in 1920 and up to the present time, the plaintiffs’ land is described as being entirely in Abington. If the plaintiffs’ adjacent Abington parcels were in Brockton and zoned for business, a provision of that city’s ordinance would *532 permit the business use to extend to North Quincy Street. 3

We assume without deciding that the Brockton zoning ordinance applies to the narrow strip and do not concern ourselves with the effect of a location of the traveled way not conforming to the official description. There is no doubt that use of the strip for business access to other land is business use. Harrison v. Building Inspector of Braintree, 350 Mass. 559, 561.

The board’s decision to deny Lapenas a variance was on the grounds that ‘1 a variance would derogate from the character of the neighborhood and would not comply with the intent of the zoning by-laws.” The grounds of the vote to deny Thompson a variance were that “the statutory conditions had not been met, and ... [a] variance would derogate from the intent of the . . . ordinance. ’ ’

The judge found the facts to be otherwise, and ruled that the statutory conditions had been met. (1) “The condition especially affecting the . . . [plaintiffs’] land does not affect generally the other land in the zoning district ... all of the land other than the land on the easterly side of North Quincy Street being located entirely within the City of Brockton.” (2) “ [L]iteral enforcement of the provisions of the Zoning Ordinance would involve substantial hardship . . . [in denying the plaintiffs] the right to use . . . [the plaintiffs’] land in Abington for the purposes for which it was zoned.” (3) Granting variances “would be without substantial detriment to the public good and without nullifying or substantially derogating from the intent or purpose of the Zoning Ordinance.”

The judge concluded that variances had been denied because of the use intended for the Abington land and ruled that the board had exceeded its authority in denying the plaintiffs access “because it disapproves of the [proposed] use.”

*533 The board was in error as to the intent and purpose of the Brockton ordinance. The ordinance could have no intent or purpose in respect of the Abington land. Construed as operative to bar any access to the plaintiffs’ Abington land for lawful use, it would be arbitrary and invalid, especially since by § 13 (b) it could not operate in this way if all the plaintiffs’ land were in Brockton. Barney & Carey Co. v. Milton, 324 Mass. 440, 449. Gem Properties Inc. v. Board of Appeals of Milton, 341 Mass. 99, 105. Jenckes v. Building Commr. of Brookline, 341 Mass. 162, 165-166. Mahoney v. Board of Appeals of Winchester, 344 Mass. 598, 601-602.

We recognize that the Abington business area is not part of the Brockton zoning scheme and that, consistently with that scheme, the classification of the plaintiffs’ land might have been for other than business use. Reasonable access roadways over the Brockton strip will, however, leave the residential area across North Quincy Street protected by an area free of buildings. We think that Brockton’s zoning interests support no more than this.

In the circumstances, the plaintiffs are entitled to relief from the literal operation of the zoning ordinance. In the absence of variances, this might be sought in proceedings under G. L. c. 231A (Woods v. Newton, 349 Mass. 373, 376-377), or c. 185, § 1 (j1/2), and c. 240, § 14A.

In the cases at bar, however, the plaintiffs sought variances. Although, as it turns out, the plaintiffs’ rights of access do not depend on variances, it is not inappropriate that the apparent conflict between the imperative need of access to abutting land, zoned for business, and the Brock-ton ordinance be removed of record in variance proceedings. The plaintiffs do not seek to exempt their Brockton parcels from all residential district restrictions.

As an erroneous construction of the Brockton ordinance underlay the board’s denials, we might, as in Chater v. Board of Appeals of Milton, 348 Mass. 237, 246, remand the cases to the board for further consideration. We conclude that, in the unusual circumstances, this is an unnecessary step. We said in Pendergast v. Board of Appeals of Barn- *534 stable, 331 Mass. 555, 559-560, “We think no one has a legal right to a variance. If a case should come to us in which an owner had been denied a variance solely upon a legally untenable ground and the board should indicate that . . . [otherwise] the variance would have been granted, perhaps the court could give relief. But no such case is before us; Neither ... [is this] a case where the decision ... is unreasonable, whimsical, capricious, or arbitrary and so illegal. We make no implication as to such a case, if such a case can arise.” See Ferrante v. Board of Appeals of Northampton, 345 Mass. 158, 162. Compare Mahoney v. Board of Appeals of Winchester, 344 Mass. 598, 601-602. (Discretionary denial of a permit under G. L. c. 40A, § 4, on an untenable ground annulled); accord, Lombard v. Board of Appeal of Wellesley, 348 Mass. 788.

Here the board has not expressly indicated that, except for the untenable grounds stated, it would have granted the variances. Not to do so, however, would, we think, be capricious and arbitrary. Mahoney and Lombard cases, supra. An intention so to act is not to be imputed to the board. Nor does full recognition of the basic principle stated in the Pendergast case, and of the functions of the board and the court in respect to the granting of variances, require that the present disposition of these appeals leave open the possibility of such action. The granting of the variances in the circumstances involves an exercise of discretion by the board only to the extent of electing to record the board’s recognition of the legal rights of access. An order requiring this action does not significantly invade the board’s powers.

We construe the final decrees to determine that the plaintiffs are entitled to variances. The decrees are to be modified to order remand of the cases for action to comply with such determinations. As so modified, the decrees are affirmed.

So ordered.

For convenience we refer to Paul and Helen Lapenas who, as husband and wife, are the plaintiffs in the first suit, as one plaintiff.

Zoning ordinance § 13 (b): "Where a district boundary line divides a lot in a single ownership prior to November 29, 1920, the regulations for the less restricted portion of such lot may extend to the entire lot, but not more than twenty-five feet beyond the boundary line of the more restricted district. ’ ’