Question 1 - Page 27 - Finding Mistakes in Percentages - Chapter 1 Class 8 - Fractions in Disguise (Ganita Prakash II)

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Question 1 - Page 27 Ariba and Arun have some marbles. Ariba says, “The number of marbles with me is 120% of the marbles Arun has”. What would be an appropriate statement Arun could make comparing the number of marbles he has with Ariba’s?This is the ultimate trick of reference points! Let Arun's marbles =𝒙. Thus, Ariba's marbles =𝟏.𝟐𝒙 (which is 120% ). If Arun wants to compare his marbles to Ariba's, Ariba becomes the new "base" (the denominator). (𝑨𝒓𝒖𝒏^′ 𝒔 𝑴𝒂𝒓𝒃𝒍𝒆𝒔)/(𝑨𝒓𝒊𝒃𝒂^′ 𝒔 𝑴𝒂𝒓𝒃𝒍𝒆𝒔)=𝑥/1.2𝑥 =𝟏/(𝟏.𝟐) =1/(12/10) =10/12 =𝟓/𝟔 To turn 𝟓/𝟔 into a percentage, multiply by 100: 𝟓/𝟔×𝟏𝟎𝟎≈𝟖𝟑.𝟑𝟑% Thus, Arun should say, "The number of marbles with me is about 83.33% of the marbles Ariba has." (Or, more simply, "I have 5/6 of the marbles you have!"). It is not 𝟖𝟎% !