COMMERCIAL ARITHMETIC

SIMPLE PROBLEMS IN PROFIT SHARING
1. A, B and C are partners in a firm and their respective capitals are Rs.45,000/-, Rs.60,000/- and  80,000/-.  If the profits at the end of the year amount to Rs.14,800/-, find the share of each in the profit.  [Rs.3600/-, Rs.4800/- and Rs.6400/-]
2. A, B and C invested 50,000/-, Rs.40,000/- and Rs.90,000/- respectively in a business.  At the end of the year, A received 8,000/- as his share in the profit.  Find the total profit.  Also find B’s and C’s share in the profit.  [Total profit -Rs.28,800/- and B’s and C’s shares of profit are Rs.6,400/- and Rs.14,400/-]
3. A, B and C started a business with a total capital of Rs.1,00,000/-.  At the end of the year, the profits received by A, B and C were Rs.2,000/-, Rs.3,000/- and Rs.5,000/- respectively.  Find the amount of capital invested by B. [Rs.30,000/-]
4. A started a stores by investing a certain capital.  After 2 months he admitted B as a partner who invested the same amount.  Finding the need for more capital for the expansion, they invited C into their partnership after 4 months, on the condition that he brings in the same amount of capital as they had.  At the end of the year when accounts were finalized, they showed a profit of Rs.25,200/-.  How much was the share of each in the profit? [Rs.10,800/-, Rs.9,000/-, Rs.5,400/-]
5. Ramanbhai started a business with a capital of Rs.20,000/-.  After 5 months Nitinbhai accepted his partnership with a capital of Rs.18,000/-.  After 9 months from the starting of the business, Vipulbhai joined the two with a capital of Rs.12,000/-.  At the close of the year, the business realized a profit of Rs.20,100/-.  How much was the share of each in the profit? [Rs.12,000/-, Rs.6,300/- and Rs.1,800/-]
6. A and B are partners in a company having capitals in the ratio and the profits received by them are in the ratio .  If B’s capital in the company was for 16 months, how long was A’s?  [25 months]
7. Amar, Akbar and Antony are partners in a business.  Amar’s and Akbar’s capitals are in the ratio and Akbar’s and Antony’s capitals are in the ratio .  At the end of the year, the profit is Rs.62,000/-.  How should it be distributed among the three partners?  [Rs.30,000/-, Rs.24,000/- & Rs.8,000/-]
8. Mr. Wadia and Mr. Jokhi started a business with a capital investment of Rs.55,000/- and Rs.35,000/- respectively.  After 5 months, Mr. Wadia put in Rs.10,000/- more to his capital while Mr. Jokhi withdrew 5,000/- from his existing capital.  At the end of the year, the profit was Rs.11,150/-.  Determine the proportionate distribution of the profit between the two partners.  [Rs.7,300/- and Rs.3,850/-]
9. A and B started a business with capitals in the ratio .  After 8 months, A withdrew 20% of her capital and B put in an equal amount in addition to her earlier capital.  If at the end of the year A’s share of profit was Rs.11,200/-, find the total profit and B’s share of profit.  [Rs.21,600/- and Rs.10,400/-]
10. Nagesh and Mangesh started a partnership firm by putting a capital of Rs.1,00,000/- and Rs.2,00,000/- respectively.  At the end of the first year, there was a profit of 45,000/-.  Nagesh withdrew Rs.5,000/- from his share of profit and Mangesh withdrew Rs.20,000/- from his share of profit.  At the end of the second year, there was a profit of Rs.48,000/-.  How should it be distributed between the partners?  [Rs.16,500/- and Rs.31,500/-]
11. A, B, C start a business by investing Rs.1,50,000/-, Rs.1,20,000/- and Rs.50,000/- respectively.  As per their agreement, each of them gets 3% interest on the capital.  C offers to practically manage the business on a day-to-day basis, hence he is also given a salary of Rs.2000/- per month.  They decide to share the net profit (after deducting the interest and the salary) in the proportion of their capitals.  The gross profit at the end of the year is Rs.81,600/-.  Find each partner’s share in net profit.  Also find the gross amount received by each of them (i.e., each partner’s share in gross profit).  [Rs.27,000/-, Rs.21,600/-, Rs.33,000/-]
12. A and B are partners in a business with capitals Rs.45,000/- and Rs.36,000/- respectively.  They admit C in the business, giving him th share in the total profit.  How much capital should C invest?  What is the proportion in which A, B and C will share the profit?  [Rs.9000/- and ]
13. A, B, C are partners sharing profits in the proportion respectively.  C retires from the business and removes his capital from the business.  What will be the ratio in which A and B will share the profit?  []
14. A, B and C start a business by investing Rs.50,000/-, Rs.2,00,000/- and Rs.2,00,000/- respectively.  A is to get a monthly salary of Rs.1,000/-, while B and C are to get interest on their capitals @ 4% p.a.  At the end of the year, there is a gross profit of Rs.39,700/- from which the salary and interest due to the partners are to be settled before distributing the net profit.  Find the gross income of each of the partners.  [Rs.13,300/-, Rs.13,200/-, Rs.13,200/-]
15. A and B are partners sharing profit in the ratio .  They admit a new partner C, giving share in the total profit.  In what proportion will A, B and C share the total profit?  []
COMMISSION & BROKERAGE
1. An agent sells goods worth 5,200/- on cash and goods worth Rs.6,000/- on credit.  If he charges 5% commission on cash sale and 8% on credit sale, how much does he receive?  [Rs.740/-]
2. A company fixed the rate of commission to its salesman as:  3% on the first Rs. 5,000/-, 5% on the next Rs. 8,000/-, 8% on the next Rs.10,000/-, 11% on the balance.  He secured sales worth Rs. 29,000/-.  Calculate the total earnings of the salesman.  [Rs.2010/-]
3. An insurance company pays its agents a commission at 20% on the first year’s premium amount.  The rate of commission reduces to 8% for the second upto the fifth year and then further reduces to 6% for the subsequent years.  A customer purchased a policy of Rs.1,00,000/- through an agent and paid for seven years the annual premium at 5% of the policy amount.  Find the agent’s total earnings for the period of seven years.  [Rs.3,200/-]
4. A merchant pays a fixed monthly salary to his agent and also a commission at 5% on the sales above Rs.40,000/-.  In a particular month, he achieved a sales figure of Rs.65,000/- and received a total remuneration of 3000/-.  Find his monthly salary.  [Rs.1750/-]
5. A merchant gives his agent 10% ordinary commission and 33 % extra commission on sales of goods above  Rs.3,000/-.  How much will the merchant receive on the total sales of Rs.4500/-?  [Rs.3,555/-]
6. The price of a radio set is Rs.550/-.  An agent charges commission at 10% on the sale of radio sets.  If he earns Rs.825/-, find the number of radio sets sold by him.  [15]
7. A salesman is paid 3% commission on credit sales and 6.5%  on cash sales.  If in a month he secured credit sales worth Rs.2,50,000/- and cash sales worth Rs.1,00,000/- then find his average rate of commission for that month.  [4%]
8. An employee gets a monthly salary plus an incentive at a certain rate on his total sales during the month.  He received Rs.11,000/- and Rs.14,600/- as total remuneration for two successive months when his sales were 50,000/- and Rs.80,000/- respectively.  Find his monthly salary and the rate of incentive.  [Rs.5000/- & 12%]
9. An agent was paid Rs.5,344/- as commission at the rate of 3% on the first 1,00,000/- and 4% on the remaining sales of toy cars.  The price of a toy car was 100/-.  Find the number of toy cars sold by the agent.  [1586]
10. A salesgirl’s rate of commission increased from 10% in a month to 12% in the next month.  Her sales also increased and the ratio of her commissions in the first and the second month was .  What was the percentage of increase in her sales.  [50%]