**Example 1.** Tom & Harry rent a pasture for 8 months. Tom puts in 85 Oxen for 3 months. How many oxen can Harry put in remaining month, if Tom pays half as much as again Harry.

**Sol :** (85 × 3)/(X × 5) = 3/2 ⇒ X = 34

**Example 2.** Vineet & Nikhil started a business of electronics items. They invest their money in the ratio of 7:5 respectively. After 5 months, Ayna joined them by investing an amount equal to Nikhil’s Share. At the end of year, they get total profit Rs. 26850. Find the profit of Ayna.

**Sol :** = First of all we will calculate the weighted ratios

⇒ Vineet = 7 × 12 = 84

⇒ Nikhil = 5 × 12 = 60

⇒ Ayna = 5 × 7 = 35

⇒ Profit of Ayna = 35/179 x 26850 = Rs.5250

**Example 3.** Karan and Aditya started a partnership business investing some amount in the ratio of 4: 7. Rohit joined them after seven months with an amount equal to that of Aditya. In what proportion should the profit at the end of one year be distributed amount Karan, Aditya & Rohit?

**Sol :** Let initial investment of Karan is 4k and Aditya is 7k, then Rohit investment is also 7k, but most important to note in this question is the time duration of investment.

Like, Karan invested for 12 months, Aditya invested for 12 months and Rohit invested for 5 months.

Karan: Aditya: Rohit = (4k × 12):(7k ×12):(7k × 5)

= 48 : 84 : 35

**Example 4.** Shakshi started a business with Rs. 42000 and is joined afterwards by Rohini with Rs 84000. After how many months did Rohini join if the profits at the end of the year are divided equally?

**Sol :** Let Rohini joins after x months.

Then Rohini’s investments was for (12-x) months

Since the profits was divided equally.

42000 × 12=84000(12-x)

x=6

Rohini joined after 6 months.

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**Example 5.** Joe started a hardware business by investing his money Rs. 50,000. After six months, Jack joined her with a capital of Rs. 40,000. After 4 years, they earned a profit of Rs. 59,500. What was Joe's share in the profit?

**Sol :** Joe : Jack = (50000 × 48 : 40000 × 42) = 10 : 7.

Jack's share = Rs. (∴ 59500 × (7/17)) = Rs. 24,500.

**Example 6.** Neha & Megha invests in a partnership business in the ratio 4:5. If share of Neha is Rs. 1900 and also 10% of profit goes to charity. Find the total profit.

**Sol :** After charity 90% of the profit is to be divided in the ratio 4:5.

Let total profit is x

Neha’s share is 4/9 of 90%x

So 4/9 of .9x = 1900

x = 1900 x9/.9 x4 = Rs.4750

**Example 7.** A began a business with Rs. 35,000. He was joined afterwards by B with Rs. 45000. For how much period does B join, if the profits at the end of the year are divided in the ratio of 4 : 3 ?

**Sol :** Suppose B joined for k months. Then, (35000 × 12)/ (45000 × k) = 4/ 3. Or k = (35000 x 12 × 3) / (45000 × 4) = 7.

So, B joined for 7 months.

**Example 8.** Heena and Meena started a software business jointly. Investment of Heena's was four times the Meena’s Investment. Meena invested for 3 times of the time period of Heena’s investment. If Meena’s get Rs.6000 as her profit, then find out the total profit.

**Sol :** Suppose Heena invested Rs.4y for x months. Then, Meena invested Rs. y for 3x months.

So, Heena: Meena = (x × 4y) : (3x × y) = 4xy : 3xy = 4 : 3

So Meena will get 3/7 of the profit which is equal to Rs.6000

Let total profit = x

So 3/7 x = 6000

x =6000 x 7/3 =Rs.14000

**Example 9.** Mayank and Blossom went to a picnic at hill station. They had 10 and 8 breads respectively. Neetu joined them and contributed Rs. 54. They divide breads equally. How much amount should be paid by Neetu to Mayank?

**Sol :** Total number of breads with Mayank and Blossom is 18. So, each of them will have 6 breads each.

The cost of 6 breads is Rs. 54.

Therefore, cost of 1 bread is 54/6= Rs. 9

Neetu got 4 breads from Mayank. So she has to pay = 9 × 4 = Rs. 36

These are the some solved problems on partnership, which helps you to understand the question.

Now let see some more Problems on Partnership.