(4) ‘A’  and  ‘B’  started a business in partnership investing  the  same amounts. They made a total profit of  Rs. 8000. ‘A’  got Rs. 6000 out of  the profits for his investment for  12  months. For how long did ‘B’ invest ?

Soln. A’s  profit  =  Rs. 6000         B’s profit  =  8000 – 6000  =  Rs. 2000

Ratio of  profit  =  6000 : 2000   i.e.,  6 : 2.

  Rs. x  12 months  :  Rs.  x  y months   =   6 : 2

  B invests for  4 months.

(5) Mr. Vijay saved one fifth  of  his income and invested it in 3 firms in the ratio  3 : 2 : 5.  If  Rs. 5000  was his least investment,  find his income.

Soln. Saving from income are invested in the ratio  3 : 2 : 5

Least         Then           Total

2k                       10k

5000                  ( ? )

= Rs. 25000

of  his income is  Rs. 25000

 His income is Rs.  125000.

(6) A, B, C  start  a business with capitals in the ratio  .  B puts in thrice his capital at the end of  6 months.  Out of  a total annual profit of  Rs. 440, find  B’s  share.

Soln. Ratio of  capitals in the beginning  =    =  4 : 6 : 3

Suppose they originally invest  Rs. 4k,  Rs. 6k  and  Rs. 3k.

Ratio of  their investments  =  ( 4k  12 ) : ( 6k  12 + 18k  6 ) : ( 3k  12 )

=  48k : 180k : 36k  =  4 : 15 : 3.

B’s share  =   440 =  Rs.300.

(7) A  invested  Rs. 50,000 in a business.  After few months,  B  joined  him with Rs. 40,000.  At the end of  the year,  the total profit was divided between  them in the ratio 3 : 1.  After  how many months did B join ?

Soln. Suppose  B  joined after  x  months. Then, B’s money  was invested for ( 12 – x ) months.

Hence,  B  joined  after  7  months

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