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 Hint: To answer this type of problem suppose the least number is x then subtract x from each of the given numbers. At last apply the given conditions that the remainders are in continued proportion then calculate the value of by solving the algebraic equation. Complete step-by-step answer: The given numbers are 7, 17, and 47We have to calculate the least number when subtracted from each of the numbers such that the remainders are in continued proportion.Let x be the number that needs to be subtracted from these numbers to make it proportional.The new numbers will be \[7 - x,17 - x,{\text{ }}47 - x\] Since these numbers should be proportional,So their ratios will be in proportion\[\dfrac{{17 - x}}{{7 - x}} = \dfrac{{47 - x}}{{17 - x}}\] By simplification we get,\[\Rightarrow {\left( {17 - x} \right)\left( {17 - x} \right) = \left( {47 - x} \right)\left( {7 - x} \right)} \\ \Rightarrow {{x^2} - 34x + 289 = 329 + {x^2} - 54x} \\ \Rightarrow {20x = 40 \Rightarrow x = 2} \] Now put the value of x in \[7 - x,17 - x,{\text{ }}47 - x\] we get the numbers asThe new numbers will be 5,15,45Therefore ′2 ′ is the least number to be subtracted so that the numbers will be proportional.Note: If there are two values of x then we will choose that value of x which satisfy the condition of proportionality as the question says and discard the other one.
′2 ′ is the least number to be subtracted so that the numbers will be in proportional. What number must be subtracted from each of the numbers 9/16 and 30 so that they are in continued proportion?Expert-verified answer → x = 2 (Ans.) Therefore, 2 is subtracted from each of the numbers 9,16, and 30, so that they are in continued proportion .Which number should be subtracted from 121 16 and 21 so that resultant numbers are in continued proportion?∴ -4 should be subtracted from 12,16 and 21 so that the resultant numbers in continued proportion.What least number must be subtracted from each of 13 16 17 and 21 to make them in proportion?Answer: 1 must be subtracted from each of the number.What least number be subtracted from each of the numbers 12 17 22/32 so that the remainders may be in proportional?These numbers are in proportion which means the ratio of two numbers is equal to the ratio of the other two numbers. Hence, the least number be subtracted from each of the numbers so that the remainders may be proportional is 2.Proportions : Solve in 30 seconds - What number must be subtracted from each of 30, 50, 65 and 113What least number must be subtracted from each of the numbers 17 17 34 42 so that the ratio of first two is the same as the ratio of the next two?what least number must be subtracted from each of the numbers 14,17,34 and 42, so that the remainders may be proportional,,,,and its answer is 2 solved them.What least number must be subtracted from each of the numbers 14 17 34 and 42 so that the remainders Navy proportional?Required number = 2. that's it.What least number must be subtracted from each of the numbers 7 17 and 47 so that the reminders are in continued proportion?What least number must be subtracted from each of the numbers 7, 17 and 47 so that the remainders are in continued proportion? Let the number subtracted to be x. Therefore, the required number which must be subtracted is 2.What least number must be subtracted from each of the numbers 7 17 and 47 so that the remainders are in continued proportion * 1 point?Thus, the required number which should be subtracted is 2.What least number must be added to each of the numbers 16 7 79 and 43 so that the resulting numbers are in proportion?Thus, the required number which must be added is 5.What number must be subtracted from each of the numbers 17/20 & 24 so that the results are in continued proportion?′2 ′ is the least number to be subtracted so that the numbers will be in proportional.Which number should be subtracted from 12 16 and 22 so that resultant numbers are in continued proportion?Step-by-step explanation: Therefore, (12-×), (16-×), (21-×) are in continued proportion. Thus, the number -4 must be subtracted from 12, 16 and 21 . So that resultant numbers are in continued proportion.Which number should be subtracted from 8 14 and 26 so that the resultant numbers are in continued proportion?∴ 2 should be subtracted from 10, 18, 14, and 26 so that the resulting numbers become proportional.What number should be subtracted from each of the numbers 31 26 22 so that the remainder may be in continued proportion?Then the numbers are (31-x), (26-x) amd (22-x). Hence, -8.5 should be subtracted from each number so that the remainder is proportional.What number should be subtracted from each of number 4 10 and 28 so that the remainder may be in continued proportion?Answer: The number to be subtracted from each of the numbers 4, 10 and 28 so that they may be in continued proportion is 1.What number should be subtracted from each of the numbers 23 30 57and 78 so that the remainders are in proportion?What number should be subtracted from each of the numbers 23, 30, 57, and 78 so that the remainders are in proportion? Therefore, 6 is the number to be subtracted from each of the numbers.When a number is subtracted from the number 8 12 and 20 the remainders are in continued proportion find the number?∴ 4 can be subtracted from the numbers 8 12 20 so that the remainder are in continued proportion.What number must be subtracted from each of the Nos 14 17 21 so that the results are in GP?⇒x=2. Was this answer helpful?What least number must be added to each of the numbers 6 15 20 and 43 so that the resulting numbers are proportional?Therefore, the required number which should be added is 3.What least number must be subtracted from each term of ratio 15 19 to make the ratio 3 4?3 is the least number to be subtracted from each term of ratio 15:19 to make ratio 3:4.What least number must be subtracted from 13601 so that the remainder is divisible by 87?⇒ 13601 ÷ 87 will give you the quotient 156 and remainder 29. So, 29 is the least number subtracted from 13601 to get the number which is completely divisible by 87.What least number must be subtracted from 176 to make it a perfect square?Therefore, 7 need to subtract for make perfect square.What number must be subtracted from each of the numbers 10 12 19 24 to get the numbers which are in proportion?Answer: so subtract 4 from each of four numbers:10,12,19 and 24 to make a proportional.What least number must be added to each one of 6 14 18 38 to make them in proportion?Correct. Hence 2 needs to be added to each of the 4 numbers - 6, 14, 18 and 38 to make the resulting numbers in proportion.What number must be subtracted from each of the numbers 41 55 36 48 so that the differences are proportional?What number must be subtracted from each of the numbers 41, 55, 36, 48, so that the differencesare proportional? the answer is 61) 0 2) 1 3) 2 4) 4 5) 5 6) 6 7) 7 8) 8 9) 9 10)3 Solution Let x must be subtracted Then 14-x / 17-x = 34-x / 42-x (14-x)(42-x) = (34-y)(17-x) x^2-56x+558 = x^2-51x+578 5x = 10 x = 2 Option 3) Correct Option: 3 Best Solution (36)Surit Datta 7 years AGO Let the required number be x. Then, (14 - x) : (17 - x) : : (34 - x) : (42 - x). (14 - x) * (42 - x) = (17 - x) * (34 - x) => x^2 - 56x + 588 = x^2 - 51x + 578 5x = 10 x = 2 Required number = 2. that's it. Like? Yes (17) | No (3) viswambher 7 years AGO If you subtract 2 from 14 and 17, you get 12 and 15. If you subtract 2 from 34 and 42, you arrive at 32 and 40. The ratios 12:15 and 32:40 both simplify to 4:5 (or 4/5 or .8). Let the required number be x. Then, (14 - x) : (17 - x) : : (34 - x) : (42 - x). (14 - x) * (42 - x) = (17 - x) * (34 - x) => x^2 - 56x + 588 = x^2 - 51x + 578 5x = 10 x = 2 Required number = 2. Like? Yes (9) | No (1) Abhishek 7 years AGOLet x be subtracted from each no. (14 - x) : (17 - x) : : (34 - x) : (42 - x) i.e. (14 - x) / (17 - x) = (34 - x) /(42 - x) By cross multiplication: (14 - x) * (42 - x) = (17 - x) * (34 - x) on solving the brackets 588- 14x - 42x + x^2 = 578 - 17x - 34x + x^2 x^2 - 56x + 588 = x^2 - 51x + 578 5x = 10 x = 2 so, number 2 is subtracted from each of the no.so that remainder are in proportion. Like? Yes (7) | No Rajanikanta Pradhan 7 years AGOProportion means a/b = b/c Let the number be a Then after subtraction the numbers are 14-a 17-a 34-a 42-a Proportionality can be determined as (14-a)/(17-a)=(34-a)/(42-a) By solving we will get a=2 Like? Yes (7) | No (1) swarupa nuggu 7 years AGOLet the required number be x. Then, (14 - x) : (17 - x) : : (34 - x) : (42 - x). (14 - x) * (42 - x) = (17 - x) * (34 - x) => x^2 - 56x + 588 = x^2 - 51x + 578 5x = 10 x = 2 Required number = 2. Like? Yes (7) | No (2) SAYAN CHATTERJEE 7 years AGOif 2 is subtracted, then the no.s become 12, 15, 32, 40 now 12:15=4:5 and 32:40= 4:5 so ans is 2 (3). Like? Yes (6) | No (1) mohita verma 7 years AGOChecking by options... 14-2=12 17-2=15 34-2=32 42-2=40 remainders are... 12, 15 32, 40 12*40=15*32 480=480 thus, 2 is the correct option Like? Yes (8) | No (3) Billal Hossain 7 years AGOLet, the subtracted number=x so,14-x, 17-x, 34-x and 42-x to be proportional 14-x 34-x ----- = ------- 17-x 42-x =>(14-x)(42-x) = (34-x)(17-x) =>14*42 -56x +x^2 = 34*17 -51x + x^2 =>14*42-34*17 = 5x =>2(294-289) => 10= 5x or x=2 Therefore, Answer will be 2 Like? Yes (5) | No Aravinth kumar 7 years AGOLet the required number be x. Then, =>(14 - x) : (17 - x) : : (34 - x) : (42 - x) =>(14 - x) * (42 - x) = (17 - x) * (34 - x) => x^2 - 56x + 588 = x^2 - 51x + 578 =>5x = 10 =>x = 2 Ans= 2 Like? Yes (4) | No Karthika 7 years AGO14-x:17-x=34-x:42-x (14-x)(42-x)=(17-x)(34-x) on solving, x=2 Let the required number be x. Then, (14 - x) : (17 - x) : : (34 - x) : (42 - x). (14 - x) * (42 - x) = (17 - x) * (34 - x) => x^2 - 56x + 588 = x^2 - 51x + 578 5x = 10 x = 2 Required number = 2 Like? Yes (4) | No RUPALI DADHE 7 years AGO14-x, 17-x, 34-x and 42-x to be proportional 14-x 34-x ----- = ------- 17-x 42-x =>(14-x)(42-x) = (34-x)(17-x) =>14*42 -56x +x^2 = 34*17 -51x + x^2 =>14*42-34*17 = 5x =>2(294-289) => 10= 5x or x=2 so 12 15 32 and 40 will be proportional Like? Yes (5) | No (1) Pranati Kundu 7 years AGOLet the required number be x. Then, (14 - x) : (17 - x) : : (34 - x) : (42 - x). (14 - x) * (42 - x) = (17 - x) * (34 - x) => x^2 - 56x + 588 = x^2 - 51x + 578 5x = 10 x = 2 Like? Yes (3) | No Jawahar 7 years AGO(14 - x) : (17 - x) : : (34 - x) : (42 - x). (14 - x) * (42 - x) = (17 - x) * (34 - x) => x^2 - 56x + 588 = x^2 - 51x + 578 5x = 10 x=2 Like? Yes (3) | No sudiptaa 7 years AGOLet the required number be x. Then, (14 - x) : (17 - x) : : (34 - x) : (42 - x). (14 - x) * (42 - x) = (17 - x) * (34 - x) => x^2 - 56x + 588 = x^2 - 51x + 578 5x = 10 x = 2 Required number = 2 Like? Yes (3) | No SUSHANT KUMAR 7 years AGO14-x, 17-x, 34-x and 42-x to be proportional 14-x 34-x ----- = ------- 17-x 42-x =>(14-x)(42-x) = (34-x)(17-x) =>14*42 -56x +x^2 = 34*17 -51x + x^2 =>14*42-34*17 = 5x =>2(294-289) => 10= 5x or x=2 so 12 15 32 and 40 will be proportional Like? Yes (3) | No shubham shukla 7 years AGOon subtracting the numbers from 2 we get: 12,15,32,40 which is on proportional form as 4:5::4:5 as required. Like? Yes (3) | No ABHINAV PUSHPAM 7 years AGOLet the required number be x. (14 - x) : (17 - x) : : (34 - x) : (42 -x) (14 - x) (42 - x) = (17 - x) (34 - x) x^2 - 56x + 588 = x2 - 51x + 578 5x = 10 x = 2 Required number = 2. Like? Yes (3) | No POOJA SINGH 7 years AGOLet the required number be x. Then, (14 - x) : (17 - x) : : (34 - x) : (42 - x). (14 - x) * (42 - x) = (17 - x) * (34 - x) => x^2 - 56x + 588 = x^2 - 51x + 578 5x = 10 x = 2 Required number = 2. Like? Yes (3) | No Dinni 7 years AGOLet the required number be x. Then, (14 - x) : (17 - x) : : (34 - x) : (42 - x). (14 - x) * (42 - x) = (17 - x) * (34 - x) => x^2 - 56x + 588 = x^2 - 51x + 578 5x = 10 x = 2 Required number = 2. Like? Yes (3) | No Kethineni Vinodh 7 years AGOLet the required number be x. Then, (14 - x) : (17 - x) : : (34 - x) : (42 - x). (14 - x) * (42 - x) = (17 - x) * (34 - x) => x^2 - 56x + 588 = x^2 - 51x + 578 5x = 10 x = 2 Required number = 2. Like? Yes (3) | No SOMA NARESH 7 years AGOLet the required number be x. Then, (14 - x) / (17 - x) = (34 - x) / (42 - x). (14 - x) * (42 - x) = (17 - x) * (34 - x) x^2 - 56x + 588 = x^2 - 51x + 578 5x = 10 x = 2 option.(3) Like? Yes (3) | No RAJAT KHANDELWAL 7 years AGOlet r be the remainder that must be subtracted from each no so (14-r)/(17-r)=(34-r)/(17-r) from here r=2 Like? Yes (3) | No Abhishek Sharma 7 years AGOLet the required number be x. Then, (14 - x) : (17 - x) : : (34 - x) : (42 - x). (14 - x) * (42 - x) = (17 - x) * (34 - x) => x^2 - 56x + 588 = x^2 - 51x + 578 5x = 10 x = 2 Required number = 2. Like? Yes (3) | No ADERU CHENCHU NITHISH 7 years AGOLet the required number be x (14 - x) : (17 - x) : : (34 - x) : (42 - x) (14 - x) * (42 - x) = (17 - x) * (34 - x) => x^2 - 56x + 588 = x^2 - 51x + 578 5x = 10 x = 2 Required number = 2 Like? Yes (3) | No ayswariyauvaraj 7 years AGOif we subtract 2 from those nos.,it will be divisible by 2 14-2=12 & 17-2=15 so, 12/15=4/5 and, 34-2=32 & 42-2=40 so, 32/40= 8/10= 4/5 Like? Yes (3) | No prasanna 7 years AGOsubtracting 2 numbers will be 12,15,32,42 to show proportionality a:b::c:d ad=bc here 12x42=15x32 hence proved Like? Yes (3) | No Anuj Rai 7 years AGOLet the required number be x. Then, (14 - x) : (17 - x) : : (34 - x) : (42 - x). (14 - x) * (42 - x) = (17 - x) * (34 - x) => x^2 - 56x + 588 = x^2 - 51x + 578 5x = 10 x = 2 Required number = 2. Like? Yes (3) | No MRITUNJAY 7 years AGOsubtract 2 from each number we get 12 15 32 40 12/15=4/5 32/40=4/5 Let the required number be x. Then, (14 - x) : (17 - x) : : (34 - x) : (42 - x). (14 - x) * (42 - x) = (17 - x) * (34 - x) solving quadratic equation we will get 5x = 10 x = 2 ans=2 , option= 3 Like? Yes (4) | No (2) Chandrima Goswami 7 years AGOLet the required number be x. Then, (14 - x) : (17 - x) : : (34 - x) : (42 - x) => (14 - x) * (42 - x) = (17 - x) * (34 - x) => x^2 - 56x + 588 = x^2 - 51x + 578 => 5x = 10 => x = 2 So ans is Option 3) Like? Yes (3) | No (1) Archie 7 years AGOLet the least number be x such that (14-x):(17-x)::(34-x):(42-x) Since numbers are proportional according to question Hence, Product of mean =Product of extreme ----> (17-x)*(34-x)=(14-x)*(42-x) Solving we get x=2 Hence option 3 is correct. Like? Yes (3) | No (1) neha gupta 7 years AGOLet the number to be subtracted be x,then (14-x):(17-x)::(34-x):(42-x) Using product of extremes = product of means (14-x)(42-x)=(17-x)(34-x) 588-56x+x^2 = 578-51x+x^2 588-578=56x-51x 10=5x 2=x Therefore answer is 2. Like? Yes (3) | No (3)
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What least number must be subtracted from each of the numbers 17 17 34 42 so that the ratio of first two is the same as the ratio of the next two?
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