Doubt solve

5775 is the answer First we give the three groups separate identities A,B,C. For A we have to choose 4 students from 12. This can be done in 12C4 ways i.e. 495 ways. Now we choose 4 students for group B from 8 remaining students. This can be done in 8C4 ways i.e. 70 ways. Therefore total number of ways is 495×70 ways i.e. 34650 ways. But in the original question groups are indistinguishable. Hence we should divide 34650 by 6 (the number of ways 3 things can be placed in 3 places) 34650/6 = 5775. In the second problem the three boys are distinct so the number of ways is 34650. E.g. take a simpler problem 6 students to 3 groups. let the students be denoted by 1,2,3,4,5,6. Now if we allocate them to groups A,B,C then

1st allocation: A:1,2 B:3,4 C:5,6

2nd allocation A:3,4 B:5,6 C:1,2

If we remove the labels A,B,C the above allocations are identical as in they divide the students into same groups. however in the second problem the three boys are distinct and number of ways will be 34650

thank you.................................

Q. Daily earnings of two persons are in the ratio 4:5 and their daily expenses are in the ratio 7:9. If each saves Rs. 50 per day, their daily income in Rs. are -

   (a) (40,50)

   (b) (50,40)

   (c) (400,500)

   (d) none of these

The answer given for this quetion is (c). But how? 

let the earnings of first person be 4x then the earnings of second person will be 5x (ratio is 4:5)

let the expenses of first person be 7y then the earnings of second person will be 9y (ratio is 7:9)

4x-7y = 50;

5x-9y = 50;

two simultaneous equations in two variables

subtracting 1st from 2nd you get x-2y =0;

i.e. x=2y;

substituiting it in the 1st equation gives x=100,y=50

therefore the answer is 400,500

Hey can anyone please solve the following question..

Q. A, B, C had capitals of Rs.50000; Rs.40000; Rs.30000 respectively for carrying on business in partnership. The firm's reported profit for the year- Rs.80000. As per provisions of the Indian Partnership Act, 1932, find out the share of each partner in the above amount after taking into account that no interest has been provided on an advance by A of Rs.20000 , in addition to his capital contribution.

(a) Rs.26267 for partner B and C & 27466 for A

(b) Rs.26667 each

(c) Rs.33333 for A, Rs.26667 for B& Rs.20000 for C

(d) Rs.30000 each

                                              Ans-(a) but how?

according to Partnership act advances should be paid an interest of 6% and the rest should be divided equally among partners so 6%(20,000) = 1200 subtracting 1200 from 80000 we get 78,800. so each share of profits are 78800/3 = 26267. now A has 1200 interest he gets so B & C gets 26267 while A gets 26266 + 1200 = 27466

Why we will subtract 1200 from 80000??