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11. Amit and Babbi enter into partnership investing Rs 16,000 and Rs 12,000 respectively. After 3 months, Amit withdrew Rs 5000 while Babbi invested Rs 5000 more. After 3 more months, Chinto joins the business with a capital of Rs 21000. The share of Babbi exceeds that of Chinto, out of a total profit of Rs 26400 after one year by
  A.  Rs 3400
  B.  Rs 4600
  C.  Rs 2600
  D.  Rs 3600
     
   
View Answer

Ratio of capitals of Amit, Babbi and Chinto = (16000x3 + 11000x9):(12000x3+17000x9):(21000x6) = 7:9:6 Babbi's share = Rs 26400 x
9 / 22
= Rs 10800 Chinto's share = Rs 26400 x
6 / 22
= Rs 7200 ∴ B's share is more than C's share by Rs 3600

12. J, R and P rented a Television for one week at a rent of Rs 350. If they use it for 6 hours, 10 hours and 12 hours respectively, the rent to be paid by P is
  A.  Rs 120
  B.  Rs 250
  C.  Rs 150
  D.  Rs 130
     
   
View Answer

Ratio of rents = 6:10:12 = 3:5:6 ∴ P's share of rent = Rs 350
6 / 14
= Rs 150

13. Kamal and Naveen started a venture. Kamal investement was thrice the investment of Naveen and the period of his investment was two times the period of investment of Naveen. Naveen got Rs 4000 as profit for his investment. Their total profit if the distribution of profit is directly proportional to the period and amount is.
  A.  Rs 29000
  B.  Rs 28000
  C.  Rs 18000
  D.  Rs 26000
     
   
View Answer

Let Naveen's investment be Rs a and b months. Then, Kamal's investment is Rs 3a for 2b months ∴ Ratio of their investments = ab : 6ab = 1 : 6 Naveen's share = Rs 4000 So, Kamal's share = Rs 24000 ∴ Total profit = Rs 28000

14. Amit started a business with Rs 450 and was joined afterwards by Bhim with Rs 300. When did Bhim join if the profits at the end of the year were divided in the ratio 2:1?
  A.  3 months
  B.  1 months
  C.  6 months
  D.  9 months
     
   
View Answer

Short cut method:
Amit's capital x Amit's time in partnership / Bhim's capital x Bhim's time in partnership
=
Amit's profit / Bhim's profit
Let Bhim joined the business for y months. Then using the shortcut, we get
450x12 / 300xy
=
2 / 1
or, 300 x 2y=450 x 12 ∴ y =
450x12 / 300x2
= 9 months

15. Amit and Bhim gets a plot on rent for 10 months. Amit puts in 100 goats for 8 months. How many can Bhim put in for the remaining 2 months, if he pays half as much again as Amit?
  A.  800 goats
  B.  500 goats
  C.  400 goats
  D.  600 goats
     
   
View Answer

Let Bhim puts in y goats The ratio of Amit's and Bhim's rents = 1 : 1 +
1 / 32
= 1:
3 / 2
= 2:3 Then,
100x8 / 2xy
=
2 / 3
or, y =
100 x 8 x 3 / 2x2
= 600 goats

16. Amit and Bhim start a venture and put their capital in the ratio 7 : 9. At the end of 8 months, Amit withdraws his capital. If they receive the profits in the ratio 8 : 9, find how long Bhim's capital was used?
  A.  3 months
  B.  7 months
  C.  5 months
  D.  9 months
     
   
View Answer

Let Bhim's capital was used for y months. Using the shortcut, we get
7x8 / 9xy
=
8 / 9
or, y=
7x8x9 / 8x9
=
8 / 9
= 7 ∴ Bhim's capital was used for 7 months.

17. Amit, Babbi and Chinto invested capitals in the ratio 2 : 3 : 5, the timing of their investments being in the ratio 4 : 5 : 6. In what ratio would their profit be distributed?
  A.  30 : 15 : 8
  B.  5 : 12 : 18
  C.  8 : 15 : 30
  D.  5 : 11 : 3
     
   
View Answer

Shortcut: If investments are int he ratio of a:b:c and timing of their investments in the ratio of x:y:z then the ratio of their profits are in the ratio of ax:by:cz Here, a : b : c = 2 : 3 : 5 x : y : z = 4 : 5 : 6 Using these values in shortcut, we get Their profit ratio = ax:by:cz = 2x4 : 3x5 : 5x6 = 8 : 15 : 30

18. Amit, Babbi and Chinto invested capitals in the ratio 5 : 6 : 8. At the end of the business term, they received the profits in the ratio 5 : 3 : 12. Find the ratio of time for which they contributed their capitals.
  A.  2 : 1 : 3
  B.  4 : 5 : 1
  C.  9 : 4 : 6
  D.  3 : 1 : 2
     
   
View Answer

shortcut: If the investments are in the rattio a:b:c and profits in the ratio l:m:n, then the ratio of time will be
l / a
:
m / b
:
n / c
Here, a:b:c= 5:6:8 l:m:n = 5:3:12 Using these values in shortcut, we get: ratio of time =
5 / 5
:
3 / 6
:
12 / 8
= 1 :
1 / 2
:
3 / 2
= 2:1:3

19. Amit, Bitto and Chetan invest their capitals in a business. If the ratio of their periods of investments are 2 : 3 : 4 and their profits are in the ratio of 4 : 9 : 8. Find the ratio in which the investments are made by Amit, Bitto and Chetan.
  A.  5 : 7 : 3
  B.  2 : 3 : 2
  C.  8 : 5 : 3
  D.  1 : 4 : 7
     
   
View Answer

shortcut: If A, B and C invest their capitals in a business and the ratio of their periods of investments are t1:t2:t3 and their profits are in the ratio of l:m:n, then the capitals will be in the ratio of
l / t1
:
m / t2
:
n / t3
Here, l:m:n = 4:9:8 and t1:t2:t3 = 2:3:4, Using these values in shortcut, we get: Ratio of their capitals =
4 / 2
:
9 / 3
:
8 / 4
= 2:3:2

20. Ajay, Beena and Chinto started a venture. Ajay receives
2 / 5
of the profit and Beena and Chinto share the remaining profit equally. Ajay's income is increased by Rs 220 when the profit rises for 8% to 10%. Find the capitals invested by Ajay, Beena and Chinto.
  A.  Ajay's capital: Rs 14000; Beena's capital: Rs 8850; Chinto's capital: Rs 4250
  B.  Ajay's capital: Rs 250; Beena's capital: Rs 1450; Chinto's capital: Rs 6650
  C.  Ajay's capital: Rs 11000; Beena's capital: Rs 8250; Chinto's capital: Rs 8250
  D.  Ajay's capital: Rs 9000; Beena's capital: Rs 7150; Chinto's capital: Rs 1950
     
   
View Answer

shortcut:
A, B and C are partners. A receives
a / b
of the A's profit and B and C share the ramaining profit equally. If A's income is increased by Rs Q when the profit raises from L% to M%, then the capital invested by A is (Rs
100 x Q / M - L
) and the capital invested by B and C is Rs
(100 x Q)/(M - L) x (1 - a/b) / 2
or
A's capital / 2
(1 -
a / b
)
Here, a/b = 2/5, Q = 220, L = 8 and M = 10
Using these values in shortcut, we get
Ajay's capital =
100x220 / 10-8
= Rs 11000
Beena's capital and Chinto's capitals =
(100 x 220)/(10 - 8) x (1 - 2/5) / 2
= Rs 8250 each.

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