{"id":"aqua_rat:a3e4668009c537f74759f67f50dc1721","source_id":"aqua_rat","source_item_id":"a3e4668009c537f74759f67f50dc1721","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 pen company produces very fine quality of writing pens. Company knows that on average 10% of the produced pens are always defective so are rejected before packing. Company promises to deliver 7200 pens to its wholesaler at Rs. 10 each. It estimates the overall profit on all the manufactured pens to be 25%. What is the manufactured cost of each pen?","stimulus":"","stimulus_html":null,"stem_html":"<p>A pen company produces very fine quality of writing pens. Company knows that on average 10% of the produced pens are always defective so are rejected before packing. Company promises to deliver 7200 pens to its wholesaler at Rs. 10 each. It estimates the overall profit on all the manufactured pens to be 25%. What is the manufactured cost of each pen?</p>","rationale_html":"<p>The company is able to deliver 90% of the manufactured pens. Means to produce 7200 pens they must have to produce 8000 pens as 10% are defectives. So, let K be the manufacturing price of each pen.</p><p>Total income (including 25% profit) = 8000 *K *1.25</p><p>This same income is obtained by selling 90% manufactured pens at Rs. 10 which is equal to 7200 *10.</p><p>Thus,</p><p>8000 *K *1.25 = 7200 *10</p><p>K = Rs. 7.2. [90% of 8000 = 7200]</p><p>Option B</p>","correct_answer":["B"],"equiv_key":"3535205be3f4b1a79ad20cf1","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>Rs. 6</p>","ord":0},{"label":"B","content_html":"<p>Rs. 7.2</p>","ord":1},{"label":"C","content_html":"<p>Rs. 5.6</p>","ord":2},{"label":"D","content_html":"<p>Rs. 8</p>","ord":3},{"label":"E","content_html":"<p>None of these</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":[]}