{"id":"aqua_rat:35475d90248ba53eda4e62dc0dfc2323","source_id":"aqua_rat","source_item_id":"35475d90248ba53eda4e62dc0dfc2323","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":"A starts a business with Rs.40,000. After 2 months, B joined him with Rs.60,000. C joined them after some more time with Rs.120,000. At the end of the year, out of a total profit of Rs.375,000, C gets Rs.150,000 as his share. How many months after B joined the business, did C join?","stimulus":"","stimulus_html":null,"stem_html":"<p>A starts a business with Rs.40,000. After 2 months, B joined him with Rs.60,000. C joined them after some more time with Rs.120,000. At the end of the year, out of a total profit of Rs.375,000, C gets Rs.150,000 as his share. How many months after B joined the business, did C join?</p>","rationale_html":"<p>Assume that C was there in the business for x months</p><p>A:B:C = 40000*12 : 60000*10 : 120000*x</p><p>= 40*12 : 60*10 : 120x = 40 : 5*10 : 10x</p><p>=8 : 10 : 2x</p><p>= 4 : 5 : x</p><p>C&#x27;s share = 375000*x/(9+x) = 150000</p><p>=&gt; 375x/(9+x) = 150</p><p>=&gt; 15x = 6(9+x)</p><p>=&gt; 5x = 18 + 2x</p><p>=&gt; 3x = 18</p><p>=&gt; x = 18/3 = 6</p><p>It means C was there in the business for 6 months. Given that B joined the business</p><p>after 2 months. Hence C joined after 4 months after B joined</p><p>Answer is B</p>","correct_answer":["B"],"equiv_key":"337b89cac19fd612d2bad291","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>2 months</p>","ord":0},{"label":"B","content_html":"<p>4 months</p>","ord":1},{"label":"C","content_html":"<p>23 months</p>","ord":2},{"label":"D","content_html":"<p>24 months</p>","ord":3},{"label":"E","content_html":"<p>84 months</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":[]}