# Aptitude - Ratio and Proportion - Discussion

### Discussion :: Ratio and Proportion - General Questions (Q.No.9)

9.

The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is:

 [A]. 20 [B]. 30 [C]. 48 [D]. 58

Explanation:

Let the three parts be A, B, C. Then,

 A : B = 2 : 3 and B : C = 5 : 8 = 5 x 3 : 8 x 3 = 3 : 24 5 5 5 A : B : C = 2 : 3 : 24 = 10 : 15 : 24 5 B = 98 x 15 = 30. 49

 Mona said: (Aug 24, 2010) Explain how 8*3/5 came ?

 Rithesh said: (Oct 26, 2010) See @mona Here actually we use to find the ratio is the the ratio between c:a Beacause already a:b & b:c are given to find c:a here we got 3:5 by by taking the last digit in the ratio a:b 2:3 we took 3 by taking the first digit in the ratio b:c 5:8 we took 5 then mulltiply the ratio numbers in b:c with 3/5 then we will get

 Mukesh said: (Dec 10, 2010) How do we take 3:5 and why. Explain how 8*3/5 came ? and why.

 Kalpa said: (Dec 26, 2010) Let 3 number are X,Y,Z given X+Y+Z=98 X:Y::2:3 Y:Z::5:8 => X/Y=2/3 =>Y/Z=5/8 => X=2Y/3 =>Z=8Y/5 so,X+y+z=98 =>2Y/3+y+8Y/5=98 =>(10Y+15Y=24Y)/15=98 =>Y=1470/49 =>Y=30 so,2nd no. is 30.

 Aparna said: (Dec 26, 2010) Here's the simple method Solve it by using scaling method A B C 2 3 5 8 find the lcm of middle term,i:e 5 and 3.its 15 in order to get 15,look at upper part,3 is reqd. to be mutiplied by 5,and 5 by 3 in lower part A B C 2 3(5) 5(3) 8 ans: 2*5:3*5:8*3 10:15:24

 Karthik said: (Jan 8, 2011) Hi aparn. Its very easy to understand. Thank you.

 Daksh said: (Jan 13, 2011) Explain how B=(98*15/49) ?

 Aparna said: (Jan 30, 2011) Look at the ratio: 10:15:24 here B's part is 15 and this 15 is out of 49(10+15+24) just mutiply (15/49) by 98 to get the actual value of B

 Abhishek said: (Feb 25, 2011) Now,the most easiest and trick method can be: See, 2:3 and 5:8 are the ratios of First:Second and Second:Third, So,the Second No. should be a multiple of 3 and 5.So,3*5=15, Now, choose among the choices of answers,the correct one is [B]30. 30 is the multiple of 15(both 3 and 5)....

 Babu said: (Mar 11, 2011) Excellent Kalpa

 Ranjani said: (Mar 25, 2011) Nice aparna.

 Akila said: (Apr 28, 2011) Thanks kalpa! I understood easily.

 Ashok Sarkar said: (May 7, 2011) Thanks kalpa it's very easy to understand

 Alisha said: (Jun 22, 2011) a+b+c=98 a/b=2/3 and b/c=5/8 and hence a=2b/3 and c=8b/5 so, 2b/3+8b/5+b=98 34b+15b=98*15 49b=98*15 and finally, b=(98*15)/49=30

 Emani Karthik Reddy said: (Jul 23, 2011) Sum of numbers Ax+Bx+Cx=98->1 Ratio of first to second 2:3 second to third 5:8 the ratio A:B::C:D=2:3::5:8 find the ratio A:B:C i.e A:B:C=2:3::(5*(3/5)):(8*(3/5)). new ratio is 2:3::3:24/5 A:B:C=2:3:24/5 A:B:c=10:15:24 from 1 we get 10x+15x+24x=98 x=2 second number =15*2=30.

 Avijeet said: (Sep 5, 2011) Thanks alisha. You used awesome shortcut:).

 Vicky Singh said: (Sep 6, 2011) Thanks kalpa for solve such easy method to this question.

 Amit said: (Sep 12, 2011) Hey thanks kalpa, its very easy to understand.

 Sweet said: (Nov 5, 2011) Let a's amount= z so b's amount=1210-z now (4/15)z=(2/5)x(1210-z) => (4/15)z=484-2/5z => (4/15)z+(2/5)z=484 => by taking l.c.m (10/15)z=484 => 10z=7260 => z=726 So a's amount=z=726 and b's amount=1210-726=484 ans.

 Ankur Saxena said: (Nov 30, 2011) a/b=2/3,b/c=5/8 a+b+c=98 2b/3+b+8b/5=98 b=30

 Murali said: (Dec 8, 2011) If a:b:c=2:3:5 then the ratio of (b+c)/4:(c+a)/4:(a+b)/4 is? Can any one give answer for this....

 Rishikesh said: (Jan 30, 2012) Thanks alisha.

 Deepi said: (Feb 4, 2012) Hi Guys, I have a shortcut method like this kind of problems see this a:b:c can be calculated easily from a:b and b:c just multiply as shown below a:b b:c ------- a*b:b*b:b*c So from the problem 2:3 is a:b and 5:8 is b:c 2:3 5:8 ------- 2*5:3*5:3*8 answer is 10:15:24 Here given is sum of three number is 98. that is 10+15+24=49 49=98 15=? => (15*98)/49 = 30.

 Nisha said: (Feb 4, 2012) Thanks kalpa.

 Deepi said: (Feb 5, 2012) SEE This carefully a:b1 - b2:c ----------- a*b2:b1*b2:b1*c=a:b:c

 Jay Namdev said: (Apr 19, 2012) There are 150 students in a class, we have only 58 rupees, if we distribute 25p and 50p amongst girls and boys respectively then what no of girls?

 Veena said: (May 1, 2012) x:y=2:3 --->1 y:z=5:8 --->2 multiply with 5 in equation 1 10:15 in equation 2 multiply with 3 15:24 10:15:24 15--? 49--98 15/49x98=30

 Poorni said: (May 2, 2012) THANKS APARNA

 Rajkumar said: (May 5, 2012) General formula A:B B:C --------------- A*B : B*B : B*C ---------------- A*B + B*B + B*C = sum Then total should be divided with this sum Ans = total / sum This ans should be multiplied with each ratios to get a desired number In the same way 2:3 5:8 ------- 10:15:24 (2*5 : 3*15 : 3*8) Then adding 10+15+24 gives 49 This 49 divides 98 98 / 49 = 2 B = 2*15 = 30 Similarly A = 2 * 10 = 20 C = 2 * 24 = 48

 Sana said: (Jun 26, 2012) Kalpa and Abhishek gave best n easy methods, thank you :).

 Amruta said: (Aug 16, 2012) Thanks kalpana:).

 Pravinbabu said: (Aug 23, 2012) Excellent Alisha

 Nena said: (Apr 5, 2013) I have a question please solve it. If A:B=2:3, B:C=4:5, and C:D= 6:7 then find the value of A:B:C:D.

 Rupam said: (Jun 8, 2013) A:B = 2:3. B:C = 5:8. (2:3)x5 = 10:15. (5:8)x3 = 15:24. A:B:C = 10:15:24. So the second number(B) is: (98*15/49) = 30.

 Sid said: (Jun 19, 2013) @jay namdev we have Rs.58. IN 58 25 paise is = 58*4 = 232. In 58 50 paise is = 58*2 = 116. Ratio of 50 paise : 25 paise 1:2. Total 150 student it means if boys is 50 then girls is 100. 100+50 =150. It means total girls in class is 100.

 Elizabeth Scaria said: (Aug 20, 2013) If a:b=m:n and b:c=p:q then a:b:c= mp:np:nq. Here, a:b=2:3 . b:c=5:8. Then a:b:c become 10:15:24. If sum of money S is divided in the ratio a:b:c then part of b is = (b/a+b+c)*S. Now here part of B become (15/49)*98 = 30.

 Chandan said: (Sep 6, 2013) A:B = 2:3. B:C = 5:8. (2:3)x5 = 10:15. (5:8)x3 = 15:24. A:B:C = 10:15:24. Let the ratio of numbers be 10x:15x:24x. According to question, 10x+15x+24x = 98. 49x = 98. x = 98/49. x = 2. Now 2nd number is 15x. i.e;15*2 = 30.

 Divi said: (Sep 10, 2013) Explain the whole problem clearly and step by step.

 Vinni said: (Dec 4, 2013) A:B = 2:3. B:C = 5:8. By short cut we get, A:B:C = 10:15:24. How we get is by using above ratios, A's value = A*B. B = B*B. C = B*C... Then as given in problem, 10x+15x+24x = 98. 49x = 98. x = 2.. So, 15x = 15*2 = 30.

 Vignesh said: (Jan 16, 2014) Instead of doing as per some formula you can solve this question right from the options given below let me explain, See the question " If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8 ". * They are asking the value of B only so whose part is 3 and 5 so if you look into the option only the number 30 will be divided by both 3 and 5 whereas other option can't just try with this method it may be useful to you. CROSS CHECKING THE ANSWER : If B is 30 then A will be 20 and C will be 48 so by adding this (20 + 30 + 48 = 98). Solution correct !

 Deva said: (Jul 29, 2014) Please tell me the easy way to solve this problem?

 Abhijith said: (Oct 13, 2014) x+y+z = 98;--> eq.1 x/y = 2/3; y/z = 5/8; x = (2y/3); z = (8y/5). Substituting new value of x and z in eq 1, => (2y/3)+y+(8y/5)=98; Taking LCM as 15; => (10y+15y+24y)/15=98; => 49y=98*15; => y=(98*15)/49; => y=2*15; => y=30.

 Shipra said: (Jan 19, 2015) Hello guys! There is a short trick for these kinds of questions. Given, A:B = 2:3. B:C = 5:8. Multiply A and B (below one) , B and B (below one) and lastly B and C (below one). We directly get 10:15:24. Now add them all i.e. (10+15+24) = 49. From formula, (98*15)/49 = 30.

 Jayadev Samantaray said: (Apr 30, 2015) Given: x+y+z = 98. x:y = 2:3 and y:z = 5:8. y = ? Here x:y = 2:3 => x/y = 2/3 => y = (3/2)x = 3x/2 (in form of x.clear). Similarly, y:z = 5:8 => y/z = 5/8 => z = (8/5) y = 8/5*(3x/2) = 12x/5 (in form of x.clear). According to question, x+y+z = 98. So, x+3x/2=12x/5 = 98. => 49x/10 = 98. => 49x = 980. => x = 20. The value of y = 3x/2 = (3*20)/2 = 30...(Ans).

 Mandeep Singh said: (May 12, 2015) A:B:C. 2:3. 5:8. We get A:B:C. A = 2X5 = 10; B = 3X5 = 15; C = 3X8 = 24; A:B:C = 10:15:24. 10x+15x+24x = 98. 49x = 98. x = 2. So B's sum is: 15X2 = 30.

 Swagger said: (Aug 5, 2015) The easiest way: a:b:c. 2:3. 5:8. So 8/5 = 1.6. So c is 1.6 times bigger than b. So 3*1.6 = 24/5. Therefore, the ratio is 2:3:24/5. Simplifying gives ratio as 10:15:24. To solve the question 10x:15x:24x = 98. 10x+15x+24x = 98, So 49x = 98, x=2. Therefore the second number is 15*2 = 30.

 Muhammad Usman Shoaib said: (Oct 29, 2015) If are is the remainder when a positive integer is divided by a single- digit prime integer, what is the largest possible value of are? Options : A 6, B 7, C 8, D 9 and E : It cannot be determined from the information above.

 Guru said: (Dec 5, 2015) Why should take 8?

 Bhuvana said: (Dec 12, 2015) @Sid. How can you say total 150 members?

 Aditya Jain said: (Apr 13, 2016) Let the three ratio be = A:B:C. A:B = 2:3. B:C = 5:8. Now A:B:C = 10:15:24 (2*5 = 10, 3*5 = 15, 3*8 = 24). Now 10 + 15 + 24 = 49. B = 98 * 15/49. = 30.

 Rashmi said: (Apr 30, 2016) @Rajkumar. Thanks for giving the best and the most simple way to solve this question.

 Ayush Jain said: (May 18, 2016) Given, A : B : C = 98. A : B = 2 : 3 ---------------> Eq.1. B : C = 5 : 8 ---------------> Eq.2. Now Multiply Eq.1 by 5 and Eq.2 by 3 to get B common; Then, A : B = 10 : 15. B : C = 15 : 24. Then, A : B : C = 10 : 15 : 24. So, 10X + 15X + 24X = 98. 49X = 98. X = 2. Then, the Second Number is 15X. i.e B = 15 * 2 = 30 => Ans.

 Anjali Sharma said: (Jul 3, 2016) It is very easy A : B = 2 : 3, B : C = 5 : 8. Multiply this 2 3 5 8 _______ 10 15 24 _________ Then, 98 * 15 / 49 = 30.

 Niroj Kumar Sahooo said: (Jul 12, 2016) Thank you @Alisha.

 Shubham said: (Jul 19, 2016) @Anjali Sharma. Please explain this, 98 * 15/49, from where this 49 come?

 Waqar Ahmad said: (Aug 6, 2016) Well explained @Alisha.

 Ankit said: (Aug 9, 2016) Why multiply with 8x3 as we multiply first two with 5?

 Prince said: (Sep 26, 2016) Of the three numbers, the ratio of first and second is 8:9 and that of second and third is 3:4. If the product of the third number is 2400, Find the second number? Please help me to find the solution.

 Ajay said: (Oct 11, 2016) A : B = 2 : 3 B : C = 5 : 8. MAKE B EQUAL BY MUL WITH 5 AND 3. 5* 2 : 3 = 10 : 15 3* 5 : 8 = 15 : 24 CON 10:15:24 NOW 10X + 15 + 24 = 98; X = 98/49; FOR B 15 * 98/49 = 30 -> Answer.

 Dennis said: (Dec 31, 2016) @Ankur Saxena, Good job your method has a different approach to the question. Thanks for explaining it.

 Tarun Dwivedi said: (Jan 23, 2017) Nice trick, Thank you @Alisha.

 Arenotravis said: (Feb 4, 2017) @Nena. A : B : C : D = 16 : 24 : 30 : 35.

 Ayeshu said: (Mar 11, 2017) Nice explanation @Ayush. Thanks.

 Oronno said: (Apr 10, 2017) Let, first numbr=a. 2nd numbr=b. 3rd numbr=c. Given that, a:b=2:3 b:c=5:8 So, a:b=2:3=5*2:5*3=10:15 b:c=5:8=3*5:3*8=15:24. Then, a:b:c=10:15:24 ( multiply by 2) a:b:c=20:30:48. Ans=30.

 Amaranathareddy said: (May 4, 2017) a : b : c = 98. a:b = 2:3. b:c = 5:8. a = 2/3b. c = 8/5b. a:b:c = 98, 2/3:b:8/5 = 98, 10b:15b:24b = 98, b = 30.

 S.Narayana said: (May 24, 2017) We have 2:3 & 5:8 but in this question, they only three numbers are there so that let us take a,b,c. 2 3-a 5-b 8-c So that 3+5+8=16. 16 = 98. 5 = ?. 5 * 98/16 = 30approx.

 Ravi said: (Aug 3, 2017) If a - b : b - c : c - d = 1 : 2 : 3, then what is the value of (a + d) : c? Can anyone solve this?

 Biplab said: (Aug 5, 2017) Thanks @Aparna.

 Akash said: (Aug 8, 2017) 1st no:2nd =2:3= (2*5) : (3*5). 10:15. 5:8= (5*3) : (8*3) 15:24 then 1st no:2nd no : 3rd no= 10:15:24 so second no = 15÷10+15+24 * 98 = 30.

 Ashwin Patil said: (Sep 23, 2017) a:b=2:3 c:d=5:8 The rule is that from ration & proportion becomes a:b ------------ ac:bc:bd from rule 2:3 ------------ 2x5:3x5:3x8 2:3 ------- 10:15:24 Second no. be 98 x 15/43= 30.

 Aisha said: (Nov 3, 2017) The sum of two numbers is 75 and their ratio is 3:2. Find the numbers. Please solve.

 Sehrish Saleem said: (Jan 27, 2018) 3+2= 5 75/5= 15 15*3= 45 15*2= 30 45+30=75 45:30 is numbers.

 Vinod said: (Feb 17, 2018) Great explanation, Thanks @Kalpa.

 Sadeesh said: (Jun 28, 2018) @Vinni. Your explanation is Best and easy to understand.

 Lipan said: (Jul 11, 2018) Thanks @Ajay.

 Pardhu said: (Jul 17, 2018) Thanks for the explanation @Shipra.

 Uday said: (Jul 24, 2018) A+B+C=98 A:B=2:3 B:C=5:8 A:B:C=10:15:24 10X+15X+24X=98 then the valve of x = 2 Now, we need 2nd no then substitute the valve of x in B then 15*2=30.

 Akash said: (Aug 30, 2018) Great and easy Thanks @Alisha.

 Ashok said: (Sep 26, 2018) a/b=2/3=>a=2/3*b. b/c=5/8=>c/b=8/5=>c=8/5*b. Given. a+b+c=98. 2/3*b+b+8/5*b=98. 10b+15b+24b/15=98. 49b=98*15. 49b=49*2*15(98 has written as 49*2). b=49*2*15/49. b=15*2. b=30.

 Sk.Rahul Basha said: (Nov 14, 2018) A:B = 2:3. 2*5 = 10,3*5 = 15,3*8 = 24. B:C = 5:8. A:B:C = 10:15:24. 10+15+24 = 49. B = 98*15/49 = 30.

 Mohammed Afnan said: (Nov 18, 2018) Let Assume, A + B + C = 98 The ratio of the first to second is 2 :3, Second to the third is 5 : 8. That Time we Should be Equal the Common Ratio, Here B is Common Ration. so, First : Second = (2:3)*5 = 10:15. Second:Third = (5:8)*3 = 15:24. Final Ration First:Second:Third = 10:15:24 = 49. Ratio = (Second Number Ratio / Total Ratio) * Total Amount. Second Number = (15/49)/98. Second Number = 30.

 Sangamesh Angadi said: (Nov 22, 2018) Simply, A:B=2:3 B:C=5:8. Then A:B:C = 10 :15 :24. so, 15 * 98/29. It will come 30.

 Vaibhav said: (Dec 8, 2018) x + y + z = 98, 2y/3 + y + 8y/5 = 98, 5y/3 + 8y/5 = 98, 25y/15 + 24y/15 = 98, 49y/15 = 98, y = 98 * 15/49, y = 30.

 Ramesh said: (Dec 28, 2018) A + B + C = 98. Divide L.H.S and R.H.S With B We get; A/B+B/B+C/B = 98/B, A/B+1+C/B = 98/B, THEN We have A/B AND B/C=5/8 then C/B=8/5. 2/3+1+8/5=98/B, SIMPLIFY WE GET B=30.

 Jeff said: (Feb 9, 2019) Thanks all for explaining.

 Ganesh R said: (Mar 5, 2019) Given : A:B = 2:3, B:C = 5:8, Ratio of A+B +C = 98. Solution: A B C. 2 3 -> 3. 5 <- 5 8. __________ 10 15 24 ( got it by multiply colomn). ___________ Now the ratio of A: B : C is 10: 15: 24. To convert any Ratio into values multiply by X. And also from given questions. 10X + 15X + 24 X = 98, 49X = 98, X = 2, To find B value from the new ratio of B i.e 15X. B= 15X, B = 15(2), B= 30.

 Avinash Dhanvijay said: (Mar 14, 2019) 2 3:5 8 10 15 24. Therefore 10+15+24 = 49 then 98/49, X = 2. Now 2nd no = 15 * 2 = 30 ans.

 Sujith said: (Mar 14, 2019) It's very simple. Given 2 : 3 and 5 : 8. i.e; 2 3 | /| |/ | 5 8 1st term a is-----> 2 * 5 = 10. 2nd term b is-----> 5 * 3 = 15. 3rd term c is------> 3 * 8 = 24. then, 10:15:24.

 Srushti Nijampurkar said: (Mar 31, 2019) Let 3 no. be A,B,C Given:- A:B = 2:3 ---> (1) B:C = 5:8 ---> (2) Multiple 1st No by 5. Multiple 2nd No by 3. New values be:- A:B = 10:15 B:C = 15:24. It means :- A:B:C = 10:15:24. Now B =(98*15/49). [Where 98 is given, 15 is B's value and 49 is the addition of total no] Then B = 30.

 Zayan said: (Apr 18, 2019) How come 24/5?

 M V Kumar said: (Jul 25, 2019) Thanks @Kalpa.

 Nikesh Prasad said: (Jul 27, 2019) Given A:B = 2:3 and B:C = 5:8. Our objective is to make the ratio of B same in both the given ratios so we multiply 5 with A:B and 3 with B:C. B becomes 15 and we get the original ratio i.e., 10:15:24.

 Akanksha said: (Aug 7, 2019) Thanks @Kalpa.

 Mandal said: (Sep 6, 2019) let the 3 numbers be x,y,z. Given is x:y = 2:3 and y:z = 5:8. So from here we see that y is the common term in both the ratio. When we will do now is make the value of "y" same in both the ratio. so in the first ratio, we will multiply the x:y with 5 and the new ratio of x:y will become x:y = 10:15. And similarly, in the second ratio, we will multiply the y:z with 3 and the new ratio of y:z will become y:z = 15:24 now from the above two newly formed ratio we see that the value of y is the same that is 15. So from here, we can write the final ratio or proportion of x:y:z as 10:15:24. So according to the given question, the sum of ratios of x,y,z is 98. Threrefore, we can write: 10n + 15n + 24n = 98. => 49n =98, => n = 2, Thus value of y(the second term) is = 15 n = 15 * 2 = 30.

 Nithi said: (Oct 6, 2019) 2:3. 2*5=10. 5*3=15. 3*8=24 5:8. 15/49*98=30. It is easy for time saving the exam.

 Tejkumar Ch said: (Oct 17, 2019) A:B =2:3. B:C = 5:8. A:B:C = 10:15:24. Therefore, A=98*10/49; B=98*15/49; C=98*24/49; Hence the result is easy.

 Rahul Kumar said: (Nov 19, 2019) x:y:z 2:3:3 ~1 5:5:8 ~2 Then multiply 1 and 2 we get 10:15:24. 10+15+24 = 98. 49 = 98. 1 = 2. 15x2 = 30.

 Dhanakar said: (Mar 28, 2020) 2:3 --5:8 _______ 10:15:24 ________ Now total sum is 98. Then 10+15+24=49. (98*15/49)=(2*15)=30.

 Saurabh Kumar said: (May 1, 2020) @All. Solution: A: B = 2:3 and B: C = 5:8. So Multiply A: B by 5 and B: C by 3. So, we got a common B. A: B = 10:15 and B: C = 15:24. Total sum = 10+15+24 = 49, Now, we want B so we simply. B = (15/49)*Sum of total numbers (GIVEN). B = (15/49)*98. we get 30.

 Rezvi said: (May 18, 2020) Well said, Thanks @Kalpa.

 Manisha said: (May 22, 2020) Let the three numbers be x, y and z. x : y : z 2 : 3 -----5 : 8. = 10 : 15 : 24 (2*5 : 3*5 : 3*8). = 10 + 15 + 24 = 49. for B = 98 * 15/49, =30.

 Jarmy said: (Jul 28, 2020) How come 49? B = 98 * 15/49.

 Nitika said: (Aug 25, 2020) a:b = 2:3, C:d = 5:8, a:b:c= 10:15:24. And 10+15+24 = 49 but their total given is 98. So, we will multiply 49 by 2(because. Their total is 98 not 49) which will be 98. Now; as in question they have asked to find the second number. So we will now multiply 15 by 2 = 30 answer.

 Kanchan said: (Sep 2, 2020) For making B in the ratio equal. A:B =5*2:3*5 B:C = 3*5:8*3 A:B:C become, 10:15:24. Now let multiple ratio by x. 10x:15x:24x. As given; 10x + 15x + 24x = 98 49x = 98. x = 2. Now the second no.is 15x. So, 15x2= 30. Therefore the Correct answer is B.