If three friends have Rs. 12, Rs. 15 and Rs. 19 with them. Their teacher asks them to give him equal amount of money so that the amounts of money left with the friends are in continued proportion. How should I calculate the amount taken from each friend? - Find 5 Answers & Solutions

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Mathematics

Question: If three friends have Rs. 12, Rs. 15 and Rs. 19 with them. Their teacher asks them to give him equal amount of money so that the amounts of money left with the friends are in continued proportion. How should I calculate the amount taken from each friend?

Posted by: Anup Kumar on: 23 Aug, 2017

5 Answers by Expert Tutors

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Answer

Assume amount to be taken from each friend = x Rs. Amount left with 1st friend = (12 - x ) Rs. Amount left with 2nd friend = (15 - x ) Rs. Amount left with 3rd friend = (19 - x ) Rs. As per the condition: ( 15 - x ) / ( 12 - x ) = ( 15 - x ) / ( 12 - x ) => ( 12 - x + 3) / ( 12 - x ) = ( 15 - x + 4) / ( 15 - x ) => 1 + 3 / ( 12 - x ) = 1 + 4 / ( 15 - x ) => 3 / ( 12 - x ) = 4 / ( 15 - x ) => 45 - 3x = 48 - 4x => x = 3 Hence amount to be taken from each friend = 3Rs (Ans) Lets Validate the answer: After taking 3 Rs from each friend - Amount left with 1st friend = (12 - 3 ) Rs. = 9 Rs Amount left with 2nd friend = (15 - 3 ) Rs. = 12 Rs Amount left with 3rd friend = (19 - 3 ) Rs. = 16 Rs So amount left with 1st friend : amount left with 2nd friend = 9: 12 = 3: 4 And amount left with 2nd friend : amount left with 3rd friend = 12: 16 = 3: 4 and both are same !! (Proved)

Answer by:

Gourab Ghanty, Bangalore

Answer

See first of all understand that continued proportion means ratio should be same and ratio of what so here is the calculation for that Ratio1 ÷ ratio2= ratio2÷ratio3 ie (12-x)\(15-x)=(15-x)/(19-x) I would suggest try by putting values of x starting from 1 simply check whether number becomes divisible or not after putting values of x reason for doing this is the calculation will be easy Otherwise doing square and all that stuff for finding value of x will be tedious job by putting 3 u will get correct answer.so each friend has given 3 rupees

Answer by:

Vatsal Shah, Ahmedabad

Answer

Each of them have the teacher x amount of money, They have (12-x), (15-x) and (19-x) money left which are in continued proportion So, (12-x)/(15-x)= (15-x)/(19-x) Or, (15-x)^2=(12-x)×(19-x) Or, 225-30x+x^2=228-31x+x^2 Or, 31x-30x= 228-225 Or, x=3 So each of them have given 3 Rs. to their teacher

Answer by:

Rajat Kanti Kuila, Bangalore

Answer

Let, each gave Rs. x. ATP, (15 - x ) ^2 = (12 - x ) * (19 - x ). Or, 225 - 30 x + x^2 = 228 - 31 x + x^2. Or, 31x - 30 x = 228 - 225; x = 3. Hence, each friend gave Rs. 3.

Answer by:

S.chandra, Kolkata

Answer

Let they gave teacher Rs x; So, (12 - x ), (15 - x ) and (19 - x ) are in continued proportion, so, (15 - x ) ^2 = (12 - x ) * (19 - x ); 225 - 30 x + x^2 = 228 - 31 x + x^2; 31x - 30 x = 228 - 225; x = 3; The amount taken from each friend is Rs. 3

Answer by:

Malay Kundu, Kolkata

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