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SSC Selection Post 2023 PYQ — Question 58

SSC Selection Post - Matriculation Level - 28 June 2023 - Shift 4 • Quantitative Aptitude • Q58

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15 men can complete a work in 15 days, whereas it takes 18 women to complete the work in 15 days. In how many days will 20 men and 9 women, together, complete the work? (Rounded off to complete number of days.)

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Correct answer: A

Explanation

The correct answer is Option 1 i.e. 8

Let the total work be W = 1 unit

1 man's 1 day's work ⇒ 15 men × 15 days = 1

⇒1 man’s 1 day’s work = 115×15\frac{1} {15 × 15 }= 1225\frac{1} {225 }

1 woman's 1 day's work ⇒ 18 women × 15 days = 1

⇒1 woman’s 1 day’s work = 118×15\frac{1} {18 × 15} = 1270\frac{1} {270}

Work done by 20 men and 9 women in 1 day = 20×1225+9×127020 \times \frac{1}{225} + 9 \times \frac{1}{270}  = 20225+9270\frac{20}{225} + \frac{9}{270} = 445+130\frac{4}{45} + \frac{1}{30}  

                                                                                = 890+390\frac{8}{90} + \frac{3}{90} = 1190\frac{11}{90}

Time = 1/work per day = 11190\frac{1}{\frac{11}{90}}= 9011\frac{90}{11}= 8.18 ⇒ 8 days (approx)