The ratio of efficiencies of A and B to do a certain work is 5:2. A takes X hours to complete the work, and C destroys the work in X + 5 hours. All three start working at 7 a.m. and finish at 1 p.m. C works only for the duration A works. Find the time taken by C alone to completely destroy the finished work.
Statement (I): A can complete <spanclass="katex"><spanclass="katex−mathml"><mathxmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>8</mn><mn>9</mn></mfrac></mrow><annotationencoding="application/x−tex">98</annotation></semantics></math></span><spanclass="katex−html"aria−hidden="true"><spanclass="base"><spanclass="strut"style="height:1.1901em;vertical−align:−0.345em;"></span><spanclass="mord"><spanclass="mopennulldelimiter"></span><spanclass="mfrac"><spanclass="vlist−tvlist−t2"><spanclass="vlist−r"><spanclass="vlist"style="height:0.8451em;"><spanstyle="top:−2.655em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="sizingreset−size6size3mtight"><spanclass="mordmtight"><spanclass="mordmtight">9</span></span></span></span><spanstyle="top:−3.23em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="frac−line"style="border−bottom−width:0.04em;"></span></span><spanstyle="top:−3.394em;"><spanclass="pstrut"style="height:3em;"></span><spanclass="sizingreset−size6size3mtight"><spanclass="mordmtight"><spanclass="mordmtight">8</span></span></span></span></span><spanclass="vlist−s"></span></span><spanclass="vlist−r"><spanclass="vlist"style="height:0.345em;"><span></span></span></span></span></span><spanclass="mclosenulldelimiter"></span></span></span></span></span> of the work in 16 hours.
Statement (II): The efficiency ratio of B to C is 5:1.
Which of the following is true?
