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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Two taps can fill a cistern in 20 minutes and 30 minutes... tagged by: BTGmoderatorLU ##### This topic has 3 expert replies and 0 member replies ### Top Member ## Two taps can fill a cistern in 20 minutes and 30 minutes... Two taps can fill a cistern in 20 minutes and 30 minutes. The first tap was opened initially for x minutes after which the second tap was opened. If it took a total of 15 minutes for the tank to be filled, what is the value of x? A. 5.0 B. 7.5 C. 9.0 D. 10.0 E. 12.5 The OA is B. I know the rate of the first tap is 1/20 minutes, and the rate of the second tap is 1/30. Then, the first was working x/20 minutes, and after which the second tap was opened. The total time was 15 minutes. I stuck here. I'm confused by this PS question. Experts, any suggestion? Thanks in advance. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Top Reply LUANDATO wrote: Two taps can fill a cistern in 20 minutes and 30 minutes. The first tap was opened initially for x minutes after which the second tap was opened. If it took a total of 15 minutes for the tank to be filled, what is the value of x? A. 5.0 B. 7.5 C. 9.0 D. 10.0 E. 12.5 The OA is B. I know the rate of the first tap is 1/20 minutes, and the rate of the second tap is 1/30. Then, the first was working x/20 minutes, and after which the second tap was opened. The total time was 15 minutes. I stuck here. I'm confused by this PS question. Experts, any suggestion? Thanks in advance. Hi LUANDATO. Let's continue your explanation. The first tap rate is 1/20 per minute. The second tap rate is 1/30 per minute. Now, we have to set the following equation: $$rate\ tap\ 1\ during\ x\ \text{minutes}\ +\ \left(time\ both\ taps\ worked\ together\right)\left(rate\ tap\ 1\ +\ rate\ tap\ 2\right)$$ $$=\ whole\ \text{tank}$$ $$\frac{x}{20}+\left(15-x\right)\left(\frac{1}{20}+\frac{1}{30}\right)=1\$$ $$\frac{x}{20}+\frac{15-x}{20}+\frac{15-x}{30}=1\ \Leftrightarrow\ \ \frac{15}{20}+\frac{15-x}{30}=1$$ $$450+20\left(15-x\right)=600\ \Leftrightarrow\ \ 300-20x=150\ \Leftrightarrow\ 20x=150\ \Leftrightarrow\ x=7.5$$ This is why the correct answer is the option B. I hope this answer may help you. If you have a doubt, let me know. Regards. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. ### GMAT/MBA Expert Legendary Member Joined 20 Jul 2017 Posted: 503 messages Followed by: 11 members Upvotes: 86 GMAT Score: 770 For the first x minutes, the first tap works alone at a rate of 1 cistern/20 minutes. We can express the total amount filled in this time as: $$x\ \min\left(\frac{1\ cistern}{20\ \min}\right)$$ For the remainder of the 15 minutes (in other words, for 15 - x minutes), the two taps work together at their respective rates. We can express the total amount filled in this time as: $$\left(15\ -x\right)\ \min\left(\frac{1\ cistern}{20\ \min}+\frac{1\ cistern}{30\ \min}\right)$$ If we add the total amount filled in the first x minutes to the total amount filled in the remained of the 15 minutes, we should get one full cistern: $$x\ \min\left(\frac{1\ cistern}{20\ \min}\right)+\left(15\ -x\right)\ \min\left(\frac{1\ cistern}{20\ \min}+\frac{1\ cistern}{30\ \min}\right)=1\ cistern$$ Or with our units cancelled: $$x\left(\frac{1}{20}\right)+\left(15\ -x\right)\left(\frac{1}{20}+\frac{1}{30}\right)=1$$ Then we simplify to solve for x: $$\frac{x}{20}+\frac{15-x}{20}+\frac{15-x}{30}=1$$ $$\frac{3x}{60}+\frac{45-3x}{60}+\frac{30-2x}{60}=1$$ $$3x+45-3x+30-2x=60$$ $$75-2x=60$$ $$2x=15$$ $$x=7.5$$ So the value of x is 7.5. _________________ Erika John - Content Manager/Lead Instructor https://gmat.prepscholar.com/gmat/s/ Get tutoring from me or another PrepScholar GMAT expert: https://gmat.prepscholar.com/gmat/s/tutoring/ Learn about our exclusive savings for BTG members (up to 25% off) and our 5 day free trial Check out our PrepScholar GMAT YouTube channel, and read our expert guides on the PrepScholar GMAT blog ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2950 messages Followed by: 19 members Upvotes: 43 BTGmoderatorLU wrote: Two taps can fill a cistern in 20 minutes and 30 minutes. The first tap was opened initially for x minutes after which the second tap was opened. If it took a total of 15 minutes for the tank to be filled, what is the value of x? A. 5.0 B. 7.5 C. 9.0 D. 10.0 E. 12.5 We are given that the rate of the first cistern is 1/20 and the rate of the second cistern is 1/30. The first tap worked for 15 minutes, and the second tap worked for (15 - x) minutes. Thus: (1/20)(15) + (1/30)(15 - x) = 1 3/4 + (15 - x)/30 = 1 Multiplying the entire equation by 60, we have: 45 + 30 - 2x = 60 2x = 15 x = 7.5 Answer: B _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. 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