Mrs Bouncer, a London lodging-house keeper, is letting an apartment to a double tenantry – to Box, a printer on a daily newspaper, and to Cox, a journeyman hatter, the former occupying the room during the day, the latter during the night. They invariably meet on the stairs of the lodging-house when one comes in from work as the other is going out, but neither has any idea that Mrs Bouncer is letting his room to the other. Cox, suspicious that Mrs Bouncer has been using his flat during the day, complains to her that his coal keeps disappearing and there is "a steady increase of evaporation among my candles, wood, sugar and lucifer matches." He also complains that his room is continually full of tobacco smoke. Mrs Bouncer gives various excuses – among others, that Box, who, she says, occupies the attic, is a persistent smoker, and that his smoke must come down the chimney. Cox departs for his work at the hat shop, and on the stairs passes Box who is returning from the night shift at the newspaper.
Box has brought home with him a rasher of bacon, which he at once prepares to cook. He lights the fire, is indignant that his matches have been used and his candles burnt low; for, being at home only during the day, he suspects Mrs Bouncer of these depredations. Leaving his bacon to cook, he retires to bed for a short nap. Cox then returns, having been given the day off by his employer. He has bought a mutton chop and, going to cook it on the gridiron, finds the fire already lit and the rasher of bacon on the gridiron. He removes it, puts his chop in its stead, and hurries into an adjoining room for a plate. The slamming of the door awakens Box, who, recollecting his bacon, leaps from the bed, and finds the chop where he had left the rasher. He angrily seizes the chop, flings it from the window, and leaves the room to fetch a plate. Cox re-enters, and, in lieu of his chop, discovers the rasher, which follows the chop out of the window. Box and Cox meet, each imagining the other to be an intruder, each pulling from his pocket the last week's receipt for rent, and each clamouring loudly for redress from the landlady. Mrs Bouncer is forced to explain the mystery, and she throws herself on the kindness of Box and Cox by promising either of them a handsome second floor back room, which she hurries off to prepare.
Frustrated, Box asks, "Hark ye, sir – can you fight?" Cox answers, "No, sir." Box: "No? Then come on!" Agreeing, however, that they have no quarrel with each other, and that the whole mess is Mrs Bouncer's fault, Box and Cox converse civilly. It emerges that Cox is about to be married to a widow, Penelope Anne Wiggins, a prosperous proprietress of bathing machines at Margate and Ramsgate. Box is astonished, as he too had once been engaged to Mrs Wiggins, but, he reveals, he had struck on an ingenious plan to escape her clutches: he had pretended to commit suicide by drowning. Cox is equally reluctant to marry her. The two argue about which of them is obliged to do so, and eventually they call for pistols. When Mrs Bouncer goes to bring them, Cox cries, "Stop! You don't mean to say ... that you keep loaded fire-arms in the house?" "Oh, no", says Mrs Bouncer, "they're not loaded". Cox: "Then produce the murderous weapons instantly!" Meanwhile, the two agree to cast dice; the loser must marry Penelope Anne. Both have loaded dice, and at each successive throw they continue to throw sixes. The dice are then changed for shillings. At every toss each man's coin lands on heads, as both contestants are using double-headed coins.
The impasse is broken when a letter arrives from Margate stating that Penelope Anne has drowned in a boating accident, and has left her property to her intended husband. Box and Cox now argue their claims to the bathing machines, but finally they agree to split the fortune. Now a second letter arrives, which states that Penelope Anne is quite safe and is on the road to London to claim her lover. Escape is now hopeless, and Box and Cox are in despair. A vehicle arrives, a knock resounds at the door, and Box and Cox place their backs to the door. Penelope Anne goes away again, leaving another letter revealing that she has decided to marry Mr Knox, an admirer nearer her own age. Box and Cox are delighted, and their happiness is completed by the realisation that they are brothers, who have been long separated (Box: "Have you such a thing as a strawberry mark on your left arm?" Cox: "No!" Box: "Then it is he!"). They reject the second-floor back room and determine to reside permanently in the same room, and under the tenancy of the same landlady.

Question: Why do Mr. Box and Mr. Cox argue about Penelope Anne?
Answer: Neither one wants to marry her.
Alternative answer: They are both obliged to marry her because they are both engaged to her