 Important for :
1
P starts business with Rs.4500 and after 9 months, Q joins with P as his partner. After a year, the profit divided in the 3 : 5. What is Q's contribution in the capital?
» Explain it
D
 Let Q's Capital be Rs. x. Then = 4500 ×12 3x

 = 4500 × 12 = 3 ⇒ x = 4500 × 12 × 5 3x 5 3 × 3

⇒ 1500 x 4 x 5 ⇒ Rs. 30,000.

Hence, option D is correct.

2
P and Q started a retail store with initial investments in the ratio 5 : 6 and their annual profits were in the ratio 2 : 3. If P invested the money for 8 months. For how many months did Q invest his money?
» Explain it
D
Suppose P invested Rs. 5x for 8 months and Q invested 6x for y months then,

 5x × 8 = 2 ⇒ y = 40x × 3 6x × y 3 6x × 2

 y = 120x ⇒ y = 10. 12x

Hence, option D is correct.

3
P and Q enter into partnership. P invests some money at beginning, Q invests double the amount after 4 months and R invests thrice the amount after 8 months. If the annual profit be Rs.32000, R's share is?
» Explain it
E
Let P's investment be Rs. x. then ratio of capitals = (x × 12) : (2x × 8) : (3x × 4)

⇒  12x : 16x : 12x  ⇒ 3x : 4x : 3x

 ∴ R's share  = Rs [ 32000 × 3 ] ⇒ Rs 9600. 10

Hence, option E is correct.

4
P, Q, R hired Taxi for Rs. 680 and used it for 3, 5, 9 hours. respectively hire charges paid by Q are:
» Explain it
B
P : Q : R = 3 : 5 : 9

Hire charges paid by Q

 = Rs [ 680 × 5 ] ⇒ 40 × 5 = Rs 200. 17

Hence, option B is correct.

5
P & Q entered in to partenership P investing Rs 8000 and Rs 6000 respectively. After 3 months P withdrew Rs 2000 while Q invested Rs 2000 more. After 3 more months, R joins the business with a capital of Rs 11000. The share of Q exceeds that of R. Out of the a total profit of Rs 35,100 after one year by.
» Explain it
B
P : Q : R = (8000 × 3 + 6000 × 9) : (6000 × 3 + 8000 × 9) : (11000 × 6)

⇒ (24000 + 54000) : (18000 + 72000) : (6600)

⇒ 78000 : 90000 : 66000

⇒ 26 : 30 : 22

⇒ 13 : 15 : 11

Difference of Q's & R's shares

 = Rs ( 35100 × 15 – 35100 × 11 ) 39 39

⇒  Rs.(900 × 15 – 900 × 11)  ⇒  13500 – 9900   ⇒  Rs 3600.

Hence, option B is correct.