**Q1. A, B and C entered into a partnership by investing Rs. 12000, Rs. 15000, and Rs. 18000, respectively. A is also a working partner and receiving 15% of the annual profit for his work. If B and C received Rs. 8500 and Rs. 10200 from the annual profit as their shares, what amount did A receive from the annual profit? **

(a) Rs. 10,500

(b) Rs. 11,500

(c) Rs. 11,300

(d) Rs. 14,000

**S1. Ans.(c)**

**Sol.** Capital ratio of A, B, C is 12000 : 15000 : 18000 = 4 : 5 : 6

Profit ratio of B and C = 8500 : 10200 = 5 : 6

∴ A’s share of profit =4/5× Rs. 8500 = Rs. 6800

85% of x = 6800 + 8500 + 10200

= 25500

∴ 15% of x=(25500 × 15)/85=4500

Total profit of A = Rs. 6800 + Rs. 4500 = Rs. 11300.

**Q2. A began business with Rs. 45000 and was joined afterwards by B with Rs. 54000. After how many months, did B join if the profits at the end of the year were divided in the ratio 2 : 1? **

(a) 4

(b) 5

(c) 6

(d) 7

**S2. Ans.(d)**

**Sol. **Suppose B joined after x months

∴(45000 × 12)/(54000 × (12-x) )=2/1

⇒ 45000×12

=54000×12×2-54000×2×x

⇒ 108x=54×24-45×12

⇒ 27x=54×6-45×3

⇒ 27x=324-135 = 189 ⇒ x = 7

∴ B joined after 7 months

**Q3. Ninad, Vikas and Manav enter into a partnership. Ninad invests some amount at the beginning. Vikas invests double the amount after 6 months and Manav invests thrice the amount invested by Ninad after 8 months. They earn a profit of Rs. 45000 at the end of the year. What is Manav’s share in the profit? **

(a) Rs. 25000

(b) Rs. 15000

(c) Rs. 12000

(d) Rs. 9000

**S3. Ans.(b)**

**Sol.** Let the investment of Ninad be Rs. x

∴ Investment of Vikas Rs. 2x

And investment of Manav = Rs. 3x

∴ Ratio of their investments

=x×12:2x×6:3x×4

= 12x : 12x : 12x = 1 : 1 : 1

∴ Manav’s share in the profit

=1/3×45000 = Rs. 15000

**Q4. Sarita started a business investing Rs. 50000. After six months, Abhishek joined her with Rs. 75000. After another six months Nisha also joined them with Rs. 1.25 lakh. Profit earned at the end of 2 year from when Sarita started the business should be distributed among Sarita, Abhishek and Nisha in what respective ratio? **

(a) 4 : 5 : 6

(b) 8 : 9 : 10

(c) 8 : 9 : 12

(d) 4 : 5 : 8

**S4. Ans.(b)**

**Sol.** Sarita : Abhishek : Nisha

=50000×24∶75000×18:125000×12

=2×24:3×18:5×12

=2×4:3×3:5×2=8:9:10

**Q5. Four milkmen rented a pasture. A grazed 15 cows for 4 months, B grazed 12 cows for 2 months, C grazed 18 cows for 6 months, and D grazed 16 cows for 5 months. If A’s share of rent is Rs. 1020, what is C’s share of rent **

(a) Rs. 1836

(b) Rs. 1360

(c) Rs. 816

(b) Rs. 1260

**S5. Ans.(a)**

**Sol.** 15×4 = Rs. 1020

∴18×6=1020/(15×4) (18×6) = Rs. 1836

**Q6. A started a business with Rs. 10000 and B joined him later with a capital for Rs. 40000. If at the end of the year, they both get an equal share of the profit, how many months after the business started did B join it?**

(a) 4 months

(b) 6 months

(c) 8 months

(d) 9 months

**S6. Ans.(d)**

**Sol. **Suppose, B joins A after k months.

∴ Investments of A and B are in the ratio of

10000×12:40000×(12-k)

∴10000×12=40000×(12-k)

i.e. 4(12-k)=12⇒K=9

**Q7. Three pots have the same volume. The ratio of milk and water in first, second and third pots are 3 : 2, 7 : 3 and 11 : 4, respectively. If the liquid of three pots are mixed, then the ratio of milk and water in the mixture is: **

(a) 61 : 29

(b) 61 : 30

(c) 5 : 4

(d) 29 : 61

**Q8. If p : q = r : s = t : u = 2 : 3, then **

**(mp + nr + ot) : (mq + ns + ou) is equal to: **

(a) 1 : 3

(b) 1 : 2

(c) 2 : 3

(d) 3 : 2

**Q9. If a : b = 2 : 3 and b : c = 4 : 5, find a^2:b^2:bc: **

(a) 4:9:45

(b) 16:36:45

(c) 16:36:20

(d) 4:36:20

**Q10. In a class there are z students. Out of them x are boys. What part of the class is composed of girls? **

(a) x/z

(b) z/x

(c) 1-x/z

(d) x/z-1