A-shop-keeper-gave-a-bill-to-a-customer-The-bill-was-in-two-digits-but-was-mistakenly-interchanged-thereby-undercharging-the-customer-by-45-00-If-the-sum-of-the-digits-is-9-find-the-actual-value-

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Question Number 173332 by pete last updated on 09/Jul/22

$$\mathrm{A}\mathrm{shop}\mathrm{keeper}\mathrm{gave}\mathrm{a}\mathrm{bill}\mathrm{to}\mathrm{a}\mathrm{customer}.$$$$\mathrm{The}\mathrm{bill}\mathrm{was}\mathrm{in}\mathrm{two}\mathrm{digits}\mathrm{but}\mathrm{was}\mathrm{mistakenly}$$$$\mathrm{interchanged}\mathrm{thereby}\mathrm{undercharging}\mathrm{the}$$$$\mathrm{customer}\mathrm{by}\mathrm{\$}45.00.\mathrm{If}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{the}\mathrm{digits}\mathrm{is}$$$$9,\mathrm{find}\mathrm{the}\mathrm{actual}\mathrm{value}\mathrm{of}\mathrm{the}\mathrm{bill}.$$

Answered by Rasheed.Sindhi last updated on 09/Jul/22

$$\bullet \underset{Correct}{\underbrace{(10t+u)}}-\underset{Mistaken}{\underbrace{(10u+t)}}=45$$$$\Rightarrow 9t-9u=45$$$$\bullet u+t=9\Rightarrow u=9-t$$$$9t-9(9-t)=45$$$$18t-81=45$$$$t=(45+81)/18=126/18=7$$$$u=9-t=9-7=2$$$$Original72$$$$Mistakenly27$$

Commented by pete last updated on 09/Jul/22

$$\mathrm{wow},\mathrm{you}\mathrm{are}\mathrm{wonderfu}\mathrm{sir}.\mathrm{Thank}\mathrm{you}$$

Commented by peter frank last updated on 09/Jul/22

$$\mathrm{thank}\mathrm{you}$$

Commented by Tawa11 last updated on 11/Jul/22

$$\mathrm{Great}\mathrm{sir}$$

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