X can do a piece of work in 20 days and Y can do it in 12 days. Y worked at it for 9 days. In how many days can X alone finish the remaining work?

English বাংলা
PREVIOUSLY ASKED IN:
PSC Miscellaneous Prelims 2018

Answer

5 days

Explanation

Y can complete the whole work in 12 days. So, Y's 1 day's work is 1/12. Since Y worked for 9 days, the work completed by Y = 9 × (1/12) = 3/4 of the work. The remaining work is (1 - 3/4) = 1/4. X can finish the whole work in 20 days. Therefore, the time taken by X to finish the remaining 1/4th of the work is = 20 × (1/4) = 5 days.

Key Points

  • > Total work is considered as 1 unit.
  • > Y's efficiency = 1/12 work per day.
  • > Work done by Y in 9 days = 9/12 = 3/4.
  • > Remaining work = 1 - 3/4 = 1/4.
  • > X completes 1 unit in 20 days.
  • > Time taken by X = Remaining work × X's total time = 1/4 × 20 = 5 days.
  • > LCM Method: Total work = LCM(20, 12) = 60 units. Y does 5 units/day, X does 3 units/day.

Additional Information

LCM Method Breakdown

PersonDaysEfficiency (Units/Day)Total Work (LCM)
X20360
Y12560

Memory Tips

  • LCM Magic Trick: Y does 5 units/day. In 9 days, Y completes 45 units. Remaining work = 60 - 45 = 15 units. Since X does 3 units/day, X will finish the rest in 15 ÷ 3 = 5 days.
Mathematics Time and Work Medium

Related Questions

04

একটি শ্রেণিতে মোট ছাত্রছাত্রীর মধ্যে \( \frac{5}{9} \) অংশ মেয়ে এবং বাকিরা ছেলে। যদি মেয়েদের \( \frac{1}{4} \) অংশ এবং ছেলেদের \( \frac{2}{3} \) অংশ অনুপস্থিত থাকে এবং উপস্থিত মোট ছাত্রছাত্রীর সংখ্যা 245 (সঠিক হিসাবের জন্য 244 ধরলে) হয়, তবে ওই শ্রেণিতে মোট কতজন ছাত্রছাত্রী আছে?

Medium