1. P and Q started a business by investing in the ratio of 4 : 5 respectively. After 10 months Q left the business. After 5 more months, P left the business and R joined the business by investing Rs.6400 more than P’s investment. If at the end of 20 months, the respective ratio between the profit share of P to that of Q and R together is 2 : 3, then find the total investment of P and Q together. (In Rs.)
A) 19400 B) 14400 C) 17400 D) 16400 E) 12400
18x = 14x + 6400
4x = 6400
x = 1600
total investment (P + Q) = 4x + 5x = 9x
= 9 × 1600 = 14400
Ans: B
2. A starts a business with a capital of Rs.1800. B joins the business 6 months later from the start of the business and C joins the business 8 months later from the start of the business. End of the year their respective share in profit was in ratio of 6 : 5 : 5. What is the sum of amount put in the business by B and C together?
A) Rs.8000 B) Rs.6500 C) Rs.7500 D) Rs.5500 E) Rs.7800
Sol: investment × time = profit
Ans: C
3. X and Y started a business with the investments in the ratio of 7 : 5 respectively. After 3 months from the start of the business Z joined and the respective ratio between the investments of Y and Z was 3 : 4. If the annual profit earned by them was Rs.20,400, what was the difference between X’s share and Z’s share in the profit?
A) Rs.2700 B) Rs.2400 C) Rs.2100 D) Rs.3200 E) Rs.3000
Ans: B
4. A and B started a business. B’s investment was Rs.6000 more than that of A. At the end of 8 months from the start of the business B left and C joined with an investment which was Rs.8000 more than that of A. If the respective ratio between total annual profit and B’s share in profit was 2 : 1, what was the investment made by A?
A) Rs.5000 B) Rs.4000 C) Rs.3000 D) Rs.2000 E) Rs.3500
Ans: D
5. Three people P, Q and R started a business by investing in the ratio of 5 : 4 : 6. After 6 months, P added more than 20% of the initial investment and R withdraws half of the initial investment. If the profit share of Q is Rs.11400, then find the total profit at the end of the year.
A) Rs.39150 B) Rs.39250 C) Rs.39350 D) Rs.39900 E) Rs.39500
Sol: P : Q : R
(5x × 6) + (6x + 6) : 4x × 12 : (6x + 6) + (3x × 6)
11x : 8x : 9x
Ans: D
Ans: E
7. A started a business. After 6 months from the start of the business, B and C joined. The respective ratio between the investments of A, B and C was 2 : 3 : 4. If the A’s share in annual profit was Rs.230 more than B’s share, what was the total annual profit earned?
A) Rs.3630 B) Rs.3850 C) Rs.2530 D) Rs.2750 E) Rs.3080
Sol: A : B : C
2x × 12 : 3x × 6 : 4x × 6
8. A and B started a business with the investments in the ratio of 2 : 7 respectively. After 6 months from the start of the business C joined and the respective ratio between the investments of B and C was 5 : 3. If the annual profit earned by them was Rs.7,548, what was the difference between B’s share and C’s share in the profit?
A) Rs.3332 B) Rs.2200 C) Rs.2600 D) Rs.2650 E) Rs.2250
Sol: A : B = 2 : 7, B : C = 5 : 3
A : B : C
10x : 35x : 21x 10x × 12 : 35x × 12 : 21x × 6
20x : 70x : 21x
Ans: A
9. A, B and C started a business with investments in the ratio of 7 : 6 : 8 respectively and the period for which they invested was in the respective ratio of 6 : 4 : 1. If the annual profit received was Rs.18,500, what was the difference between A’s share and the total share of B and C together?
A) Rs.2000 B) Rs.3000 C) Rs.3500 D) Rs.2500 E) Rs.4000
Sol: A : B : C
7 × 6 : 6 × 4 : 8 × 1
21 : 12 : 4
Ans: D
10. A started a business. After 4 months from the start of the business, B and C joined. The respective ratio between the amounts invested by A, B and C was 3 : 13 : 14. If the C’s share in annual profit was Rs.760 more than A’s share, what was the total annual profit earned?
A) Rs.3040 B) Rs.4000 C) Rs.2640 D) Rs.2520 E) Rs.2320
Sol: A : B : C
3x × 12 : 13x × 8 : 14x × 8
Ans: D
11. A and B started a business with the investments in the ratio of 7 : 4 respectively. After 4 months from the start of the business C joined and the respective ratio between the investments of B and C was 2 : 3. If the annual profit earned by them was Rs.4,050, what was the difference between B’s share and A’s share in the profit?
A) Rs.810 B) Rs.460 C) Rs.720 D) Rs.1020 E) Rs.960
Sol: A : B : C
7x : 4x
2x : 3
7x × 12 : 4x × 12 : 6x × 8
7x : 4x : 4x
Ans: A
12. A started a business. After 6 months from the start of the business, B and C joined. The respective ratio between the investments of A, B and C was 6 : 5 : 10. If A’s share in annual profit was Rs.2,100 more than B’s share, what was the total annual profit earned?
A) Rs.9,450 B) Rs.6,750 C) Rs.8,100 D) Rs.5,400 E) Rs.10,800
Sol: A : B : C
6x × 12 : 5x × 6 : 10x × 6
Ans: C
13. A, B and C invest in a business and the share of their investments are in the respective ratio of 0.5 : 0.25 : 0.125. After 4 months from the start of the business, C withdraws half of his investment. If at the end of the year profit recorded was Rs.11,400, how much was B’s profit share?
A) Rs.1,200 B) Rs.3,140 C) Rs.3,200 D) Rs.1,140 E) Rs.3,040
Sol: A : B : C
0.5x 0.25x 0.125x
2x : 1x : 1x 2x × 12 : 1x × 12 : 1x × 6 + 0.5x × 6
28x : 4x : 3x
Ans: E
14. A started a business by investing Rs.18,000. At the end of 6th month from the start of the business B joined with Rs.16,000 and at the end of 8th month from the start of the business C joined with Rs.12,000. If the B’s share in profit at the end of the year was Rs.6,320, what was the total profit received?
A) Rs.24,600 B) Rs.25,200 C) Rs.23,850 D) Rs.20,250 E) Rs.23,700
Sol: A : B : C
18000 × 12 : 16000 × 6 : 12000 × 4
9 : 4 : 2
Ans: E
