Mathmetics

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Q1.
 A , B and C invested Rs. 8000, Rs. 4000 and Rs. 8000 respectively in a business. A left after six months. If after eight months, there was a gain of Rs. 4005, then what will be the share of B ?
1) Rs.820 2) Rs.890
3) Rs.1020 4) Rs.1250
5)None of these
Answer : Rs.890
Explanation :
A : B : C = (8,000 x 6) : (4,000 x 8) : (8,000 x 8) = 48 : 32 : 64 = 3 : 2 : 4.
B's share = ( Rs. 4005/9) x 2 = Rs. 890.
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Q2.
 A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Rs. 855, what is the total profit ?
1) Rs.1200 2) Rs.1250
3) Rs.1450 4) Rs.1500
5)None of these
Answer : Rs.1500
Explanation :
Let, the total profit be Rs. 100.
After paying to charity, A's share = (Rs. 95 /5)x 3 = Rs. 57.
If A's share is Rs. 57, total profit = Rs. 100.
If A's share Rs. 855, total profit = ( 855/57) x100  = 1500

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Q3.
A,B and C are three partners  starts for a business. A invested Rs.25,000 in 2006. In 2007, he again invested an additional amount of Rs.10,000 and B joined with him Rs.35,000. In 2008, A invested another additional Rs.10,000 and C joined with them with an amount of Rs.35,000. If the total profit after end of three year is Rs.1,50,000 , then what is the share of the profit of B ?
1) Rs.25,000 2) Rs.30,000
3) Rs.50,000 4) Rs.75,000
5)None of these
Answer : Rs.50,000
Explanation : The share of the investment of three A,B and C = 
[25,000 x 12 + 35,000 x 12 + 45,000 x 12 ] : [35 x 24] : [35 x 12] = 3:2:1
So, B's share =(1,50,000/6) x 2 = Rs.50,000/.
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Q4.
In a partnership deal A puts Rs.2000 for the entire year, B puts Rs. 3000 initially and then increase it to Rs. 4000 at the ned of 4 months and C puts Rs. 4000 initially, but withdraws Rs. 1000 at the end of 9 months. How should they divide a profit of Rs. 8475 at the end of the year ?

1) Rs.1800 2) Rs.3300
3) Rs.3350 4) Rs.3375
5)None of these
Answer : Rs.3300
Explanation :
Calculate the equivalent capital for 1 month for each :
A's capital = Rs. (20002)) = Rs. 24000
B's capital = Rs. (30004 + 40008) = Rs. 44000
C's capital = Rs. (40009 + 30003) = Rs. 45000
Ratio of capitals : 24000 : 44000 : 45000 = 24 : 44 : 45
B's share = Rs .(8475 X 44 )/11 = Rs.3300
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Q5.
A & B entered into partnership with capitals in the ratio of 4 : 5. After 3 months A withdrew 1/4 of his capital and B withdrew 1/5 of his capital. The profit at the end of 10 months was Rs. 760. What is the share of A in that profit ?
1) Rs.300 2) Rs.330
3) Rs.430 4) Rs,560
5)None of these
Answer : Rs.330
Explanation :
Let A invest Rs. 4 & B invest Rs.5. A withdraws (1/4) x 4 = Rs.1
B withdraws (1/5) x 5= Rs. 1
Calculating the equivalent capital for 1 months :
A’s capital = Rs. (43 + 37) = Rs. 33
B’s capital = Rs. (53 + 47) = Rs. 43
Ratio of capitals = 33 : 43
A’s share = Rs.(760 x 30) /76 =Rs.330

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Q6.
A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. What is  the share of B in the profit ?
1) Rs.1900 2) Rs.2660
3) Rs.2800 4) Rs.2840
5)None of these
Answer : Rs.2660
Explanation :
For managing, A received = 5% of Rs. 7400 = Rs. 370.
Balance = Rs. (7400 - 370) = Rs. 7030.
Ratio of their investments = (6500 x 6) : (8400 x 5) : (10000 x 3)
= 39000 : 42000 : 30000  = 13 : 14 : 10
B's share = (7030 x 14/21 ) = Rs. 2660.
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Q7.
A, B  & C enter into a partnership invetsing Rs.3800, Rs.4200 and Rs.4000 respectively. How should a profit of Rs1800 be divided among them ?
1) Rs.570 2) Rs.650
3) Rs.600 4) Rs.630
5)None of these
Answer : Rs.570
Explanation :
Profit should be divided among the partners in ratio of their investments
The ratio of A, B and C's share = 3800 : 4200 : 4000 = 19 : 21 : 20
A's share = Rs.(1800 x 19)/60 = Rs.570
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Q8.
A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. How much  A receives out of a total profit of Rs. 35,000 ?
1) Rs.8400 2) Rs.11,900
3) Rs.13,600 4) Rs.14,700
5)None of these
Answer : Rs.14,700
Explanation :
Let C = x.
Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000
Or 3x = 36000
Or x = 12000
Then, A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
Thus,A's share = ( 3500 x 21/50) Rs. = Rs. 14,700.
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Q9.
Nirmal and Kapil started a business investing Rs. 9000 and Rs. 12000 respectively. After 6 months, Kapil withdrew half of his investment. If after a year, the total profit was Rs. 4600, what was Kapil's share in it ?
1) Rs.1900 2) Rs.2000
3) Rs.2300 4) Rs.2600
5)None of these
Answer : Rs.2300
Explanation :
Nirmal : Kapil = 9000 x 12 : 12000 x 6 + 6000 x 6 = 1 : 1. So, Kapil's share = Rs. (4600 x 1 / 2) = Rs. 2300.
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Q10.
Alok started a business investing Rs. 90000. After 3 months Shabir joined him with a capital of Rs. 120000. If at the end of 2 years, the total profit made by them was Rs. 96000, what will be the difference between their shares ?
1) Rs.7300 2) Rs.8000
3) Rs.20000 4) Rs.24000
5)None of these
Answer : None of these
Explanation :
Alok : Shabir = 90000 x 24 : 120000 x 21 = 6 : 7. 
Difference of their shares = Rs. (96000 x 7 / 13 - 96000 x 6 / 13) = Rs. (96000 / 13) = Rs. 7384.62. 

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