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Arithmetic: Partnership Test-4

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Question 1
Three partners invested capitals in the ratio 2:7:9.The time period for which each of them invested was in the ratio of the reciprocals of the amount invested .Find the share of the partner who brought in the highest capital, if the profit is Rs. 1080.
A
Rs. 120
B
Rs. 360
C
Rs. 540
D
Rs. 420
Question 1 Explanation: 
Ratio of the investments = 2:7:9
Since the time is reciprocal so the ratio will be = ½ : 1/7 : 1/9
Therefore the ratio of investment = 2 x 1/2 : 7 x 1/7 : 9 x 1/9 = 1:1:1
Therefore share of each of the partner
= 1/3 x 1080 = Rs. 360
Question 2
If Rs. 1066 are divided among A,B,C  and D such that A:B =3:4,B:C=5:6 and C:D = 7:5 , who will get the maximum ?
A
B
B
A
C
C
D
D
Question 2 Explanation: 
Given ratios are A/B = ¾ B/C = 5/6 C/D = 7/5 A/B  = 3 X 5 /4 X 5 = 15/20 B/C = 5 X 4 /6 X 4 = 20/24 B/C = 20 X 7/ 24 X 7 = 140/168 C/D = 7 X 24 / 5 X 24 = 168/120 A/B = 15 X 7 /20 X 7 = 105/140 That means A:B:C:D= 105 : 140 : 168 : 120 Hence C gets the maximum share
Question 3
The monthly income of the two people is in the ratio of 4:5 and their monthly expenditures are in the ratio of 7: 9 .If each saves Rs. 50 a month, then what are their incomes ?
A
Rs. 100, Rs. 125
B
Rs. 200, Rs. 250
C
Rs. 300, Rs. 375
D
Rs. 400, Rs. 500
Question 3 Explanation: 
Ratio of the income = 4:5
And the ratio of expenses = 7:9
Let the income = Rs. P
The incomes = 4p and 5p
Let the expenses = q
So expenses = 7q and 9q
Therefore from the given conditions
4p – 7q = 50
5p – 9q = 50
By solving these two equations, we get:
p= 100 and q = Rs. 50
Therefore the income of two persons = Rs. 400 and Rs. 500
Question 4
A sum of Rs. 370 is to be divided among Prashant(P), Maninder(M), Atish(A)  such that P’s share/ M’s share = M’s share/ A’s share = ¾ . Then P’s share is ___ ?
A
Rs. 240
B
Rs. 120
C
Rs. 100
D
Rs. 90
Question 4 Explanation: 
P’s share/ M’s share = (3 x 3)/(4 x 3)= 9/12
M’s share/ A’s share = 3 x 4/ 4 x 4 = 12/16
Therefore A : B : C = 9 : 12 : 16
Therefore Prashants’ share = 9/37 x 370 = Rs 90
Question 5
A man divided Rs. 770 among Richa, Natasha, Sona such that Richa receives 2/9th of what Natasha and Sona together receive. Then Richa’s share is___ ?
A
Rs. 140
B
Rs. 154
C
Rs.  165
D
Rs. 170
Question 5 Explanation: 
Total amount of money = 770
Richa share = 2/9(Natasha + Sona)
From the above equations, we get
Richa + 9/2 Richa = 770
11Richa = 770 x 2
Richa = 140
Therefore Richa’s share = Rs. 140
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