{"id":"aqua_rat:51cebc4721349dce222ee05a23fdc080","source_id":"aqua_rat","source_item_id":"51cebc4721349dce222ee05a23fdc080","external_id":null,"program":null,"section":"math","category_code":"PHM","category":"Preparing for Higher Math","subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":null,"scored":true,"layout_warning":null,"stem":"The height of a room to its semi-perimeter is 2:5. It costs Rs.260 to paper the walls of the room with paper 50cm wide at Rs.2 per meter allowing an area of 15 sq.m for doors and windows. The height of the room is:","stimulus":"","stimulus_html":null,"stem_html":"<p>The height of a room to its semi-perimeter is 2:5. It costs Rs.260 to paper the walls of the room with paper 50cm wide at Rs.2 per meter allowing an area of 15 sq.m for doors and windows. The height of the room is:</p>","rationale_html":"<p>Let, height= 2x metres &amp; (length+ breadth)= 5x metres.</p><p>Length of paper= (260/2)m= 130m.</p><p>Therefore, area of paper= (130*50/100)= 65m2</p><p>Area of 4 walls= (65+15)=80m2</p><p>2(length+breadth)*height=80.</p><p>Therefore, 2*5x*2x=80 or x2=4 or x=2</p><p>Therefore, height of the room= 4m</p><p>C</p>","correct_answer":["C"],"equiv_key":"a38ef5262b0e2f93d81b46f5","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>2.6m</p>","ord":0},{"label":"B","content_html":"<p>3.9m</p>","ord":1},{"label":"C","content_html":"<p>4m</p>","ord":2},{"label":"D","content_html":"<p>4.2m</p>","ord":3},{"label":"E","content_html":"<p>4.4m</p>","ord":4}],"passage":null,"attribution":{"source_id":"aqua_rat","source_name":"AQuA-RAT algebra word problems with rationales","rights_holder":"Google DeepMind and the AQuA-RAT contributors","canonical_url":"https://github.com/google-deepmind/AQuA","retrieved_from":"https://raw.githubusercontent.com/google-deepmind/AQuA/master/","attribution":"Algebra word problems from the AQuA-RAT dataset (Ling et al., 2017), published by Google DeepMind under the Apache License 2.0.","disclaimer":"AQuA-RAT items are crowdsourced algebra problems, not ACT questions. They carry five answer choices in the pre-2025 ACT Mathematics style and no ACT reporting category. Useful for drilling Preparing for Higher Math content; not a substitute for a real form.","license":"Apache License 2.0. Crowdsourced by DeepMind and published for free use, including commercially.","redistributable":true,"item_count":508},"equivalents":[]}