# Aptitude - Partnership - Discussion

### Discussion :: Partnership - General Questions (Q.No.7)

7.

A and B entered into partnership with capitals in the ratio 4 : 5. After 3 months, A withdrew of his capital and B withdrew of his capital. The gain at the end of 10 months was Rs. 760. A's share in this profit is:

 [A]. Rs. 330 [B]. Rs. 360 [C]. Rs. 380 [D]. Rs. 430

Explanation:

 A : B = 4x x 3 + 4x - 1 x 4x x 7 : 5x x 3 + 5x - 1 x 5x x 7 4 5

= (12x + 21x) : (15x + 28x)

= 33x :43x

= 33 : 43.

 A's share = Rs. 760 x 33 = Rs. 330. 76

 Deepu said: (Jan 7, 2011) How the ratio of A:B is brought out please can anybody explain ?

 N.Srikanth said: (May 29, 2011) A invests for 3 months N = 4x * 3 1/4th of capital(4x)= 4x-1/4(4x) this is for (10-3) months investment i.e Let M=(4x-(1/4)4x)*7 B investment for 3 months O =5x*3 1/5th of capital(5x)= 5x-1/5(5x) this is for (10-3) months investment i.e P=(5x-(1/5)5x)*7 Ratio: (N+M):(O+P) I think this will clear your doubt

 Snp said: (Aug 2, 2011) Atlast why we have to divide by 76 ?

 Umesh said: (Aug 8, 2011) A:B RATIO 4X : 5X. FOR THREE MONTHS A's SHARE = 4X*3 = 12X. FOR THREE MONTHS B's SHARE = 5X*3 = 15X. FOR NEXT 7 MONTHS NEW RATIO = (4X-1/4*X) : (5X-1/5*X) I. E 3X:4X. FOR 7 MONTHS A's SHARE = 3X*7 = 21X. FOR 7 MONTHS B's SHARE = 4X*7 = 28X. A's TOTAL SHARE =12+21 = 33X & B's = 15 +28 =43X. TOTAL MONEY = 760 TOTAL SHARE = 33+43 =76X. THEREFORE 76X =760 (i.e.)X= 10 (i.e.) A'S SHARE=33X =330.

 Rohit Singh said: (Nov 2, 2011) This is called a real brain teaser.

 Prashant said: (Apr 12, 2012) How to Solve (4X-1/4*X) : (5X-1/5*X) i.e 3X:4X.

 Arockiaraj said: (Aug 31, 2012) How to Solve (4X-1/4*X) : (5X-1/5*X) i.e 3X:4X

 Sindhuja said: (Sep 30, 2012) Is there any other is way to solve this sum?

 Pavithran said: (Aug 18, 2013) Its not (4x-1/4*x) guys. Its (4x-1/4*4x).

 Darshan said: (Nov 23, 2013) Withdrew means reducing the capital right?

 Bala said: (May 26, 2014) Why did you take both the capital of A and B as x (instead of x and y) ? In the question it was not mentioned that both the capitals are same know?

 Nani said: (Aug 7, 2014) They did not take the capital as x. The numbers were assumed to be 4x and 5x because their ratios were 4:5.

 Sindhu said: (Aug 22, 2014) For that (4x-1/4*x):(5x-1/5*5). We are applying like this, Assume a=4x, b=x/4, c=5, d=x/5. b*c/a*d. If we apply like this we can easily get 3x:4x.

 Roshni said: (Oct 2, 2014) Ratio = 4:5. 1/4*(4) = 1. 4-1 = 3. Therefore 4*3 months + 3*7 months = 33. 1/5*(5) = 1. 5-1 = 4. Therefore 5*3 months + 4*7 months = 43. So, gain ratio is 33:43. Total gain is 760/- A's share is (33*760)/76 = 330.

 Charmy said: (Feb 11, 2015) Why should we take 7?

 Nupoor said: (Mar 11, 2015) Couldn't get any of the method? Please explain me with simple steps.

 Sukumar Satyen said: (Jun 12, 2015) Following is Correct explanation: Given that, Investment ratio of A and B = 4:5. Let's assume that at 1st day, A's share = 4X and B's share = 5X. Let's assume that Total investment period was for 10 months and after that business ceased to exist....equation (1). Therefore, we will calculate A's total investment for 10 months. = A's investment for 3 months + A's investment for 7 months. = 4X*3/10+(4X-4X/4)*7/10. = 12X/10+21X/10. = 33X/10. Using equation (1), we will calculate B's total investment for 10 months. = B's investment for 3 months + B's investment for 7 months. = 5X*3/10+(5X-5X/5)*7/10. = 15X/10+28X/10. = 43X/10. PROFIT should be shared on basis of Total Investment for time period of 10 months, alike following ratio: -. 33X/10:43X/10.....equation (2). Let's calculate A's Share. = 33X/10/[(33X/10)+(43X/10)]*760. = 33X/10/[76X/10)]*760. = 33X*760/76X. = Rs. 330. Note: First, We can also write equation (1) as 33:43 and solve for A's share. Second, If A (or B) 's investment be one-time, then X will be larger. If A (or B) 's investment be recurring every month, then X will be smaller, until 3 months from execution of Partnership agreement. Thanks.

 Priya14 said: (Jul 9, 2015) Where does this 7 came? Explain me please.

 Shubham said: (Aug 2, 2015) @Priya. 7 is came after subtracting 3 from 10 (months).

 Jiten said: (Oct 7, 2015) How 1/4 will come? Please tell me anyone.

 Praveen said: (Jul 7, 2016) 4x*3+3x*7 : 5x*3+4x*7, => 12x+21x : 15x+28x, => 33x : 43x, => 33 : 43, A's share = 33/76*760 = 330, 330 is the answer.

 Gaurav said: (Jul 28, 2016) Thanks for the great explanations.

 Banke Bihari said: (Aug 10, 2016) Thank you @N.Srikanth.

 Karthik said: (Aug 18, 2016) The total number of ratio = 33 + 43 = 76.

 Sourabh said: (Aug 30, 2016) @Karthik. But there will be, upon 10 in all the numbers.

 Ekta said: (Sep 26, 2016) How 7 came? not getting that please explain me.

 Yogesh said: (Oct 26, 2016) Assume total capital is Rs. 900. And divide into the ratio of 4 : 5. After that A's capital = 400 and B's capital = 500. Then after deducted 1/4 and 1/5 from the respective capital. we get the ratio of 3 : 4. And divide Rs. 760 in the ratio of 3 : 4 then you can get 330 (approx).

 Ashiq said: (Feb 9, 2017) Here, it will be (4x-1/4*4x) : (5x-1/5*5x) = 3x : 4x.

 Sumit said: (Mar 15, 2017) Why 4x is multiply with 1/4?

 Sweety said: (May 1, 2017) Thanks for the given explanation.

 Asha said: (Jul 31, 2017) After reducing the capital why we again multiply with 4x i.e (4x-1/4*4x).

 Mary said: (Apr 2, 2018) Can anybody solve this? 2/5th of Anil salary is equal to Bhuvans salary and 7/9th of Bhuvans salary is equal to Chandra's salary. If the sum of the salary of all of them is 77000. Then how much is Bhuvans salary?

 Saran said: (Jun 12, 2018) @Mary. Anil's sal=x; Bhuvan's sal=y; Chandra's sal=z; As given in the que 2/5x=y; 7/9y=z; x+y+z=77000; 5/2y+y+7/9y=77000; After taking the lcm 45y+y+14y=77000*18, 60y=1386000, y=23100. So, this is the answer.

 Prasanthi Gudipati said: (Jul 22, 2018) Capitals=a:b=4:5. let their investments as 4x,5x. A:B=4x*10-(4x*(1/4)*7):5x*10-(5x*(1/5)*7), = 40x-7x:50x-7x, =33x:44x. A's share= {33/(33+44)}*760=330. So option A is correct answer.