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Question Number 182779 by Noorzai last updated on 14/Dec/22

Commented by Rasheed.Sindhi last updated on 14/Dec/22

$$\mathrm{M}+\mathrm{L}=7$$

Answered by TheSupreme last updated on 14/Dec/22

$$3(10K+L)=100M+10L+8$$$$30K+3L=100M+10L+8$$$$100M+7L-30K+8=0$$$${mod}_{10}$$$$7L+8{=}_{10}0$$$$7L{=}_{10}-8{=}_{10}2\to L=6$$$$100M+42-30K+8=0$$$$10M+5-3K=0$$$${mod}_{10}$$$$5-3K{=}_{10}0$$$$3K=5_{10}\to K=5$$$$so10M+5-15=0\to M=1$$$$L+M=6+1=7$$

Commented by Noorzai last updated on 14/Dec/22

$$Thanks$$

Answered by Rasheed.Sindhi last updated on 14/Dec/22

$$0⩽\mathrm{L}⩽9$$$$Sumofunits$$$$\Rightarrow 0⩽3\cdot \mathrm{L}⩽27$$$$3\cdot \mathrm{L}=\stackrel{\times }{8},\check{18}[3\cdot \mathrm{L}\ne 8,\because \mathrm{L}iswholenot8/3]$$$$\mathrm{L}=18/3=6$$$$Sumoftens$$$$3\cdot \mathrm{K}+1=\overline{\mathrm{ML}}=\overline{\mathrm{M}6}$$$$3\cdot \mathrm{K}=\overline{\mathrm{M}6}-1=\overline{\mathrm{M}5}$$$$3\cdot \mathrm{K}=\check{15},\stackrel{\times }{25}[3\cdot \mathrm{K}\ne 25,\because \mathrm{K}iswholenot25/3]$$$$\mathrm{K}=15/3=5$$$$\overline{\mathrm{M}6}=3\cdot \mathrm{K}+1=3\left(5\right)+1=16$$$$\mathrm{M}=1$$$$\mathrm{M}+\mathrm{L}=1+6=7$$

Answered by manolex last updated on 14/Dec/22

$$3\times L=\mathit{a}8$$$$\mathit{a}8=\stackrel{\bullet }{3}\Rightarrow a=1$$$$3\times L=18\Rightarrow L=6$$$$3\times K+1=M6$$$$3\times K=M5\Rightarrow K=5$$$$\Rightarrow M=1$$$$M+L=70$$

Answered by Rasheed.Sindhi last updated on 15/Dec/22

$$\underset{―}{\mathbf{A}\mathrm{n}\mathbf{O}\mathrm{ther}\mathbf{W}\mathrm{ay}}$$$$\overline{\mathrm{ML}8}is3-digitnumber\Rightarrow \mathrm{M}\ne 0$$$$\mathrm{M}isacarryof32-digitnumbers$$$$somaxvalueof\mathrm{M}is2$$$$\therefore \mathrm{M}=1or2$$$$0⩽\mathrm{L}⩽9$$$$\Rightarrow 0⩽3\cdot \mathrm{L}⩽27$$$$3\cdot \mathrm{L}=\stackrel{\times }{8},\check{18}[3\cdot \mathrm{L}\ne 8,\because \mathrm{L}iswholenot8/3]$$$$\mathrm{L}=18/3=6$$$$\therefore \overline{\mathrm{ML}8}=168or268$$$$\because 3\mid \overline{\mathrm{ML}8}[\because \overline{\mathrm{ML}8}=3\cdot \overline{\mathrm{KL}}]$$$$Hencefinally\overline{\mathrm{ML}8}=168$$$$So\mathrm{M}+\mathrm{L}=1+6=7$$

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