SSC CGL 2015 : Quant Quiz

1.Rs. 864 is divided among A, B and C such that 8 times A’s share is equal to 12 times B’s share and also equal to 6 times C’s share. How much did B get? 

(a) Rs. 399 

(b) Rs. 192 

(c) Rs. 288 

(d) Rs. 72

2.A, B and C entered into a business and their investments ratio was 5 : 4 : 3. After 4 months B invested Rs. 1,000 more and after 8 months C  invested Rs. 2, 000 more. At the end of one year the profit ratio was 15 : 14 : 11, then the investment of C at the beginning was 

(a) Rs. 3000

(b) Rs. 6000

(c) Rs. 4500

(d) Rs. 7500

3.A, B and C rent a pasture. A puts in 10 oxen for 7 months, B 12  oxen for 5 months and C 15 oxen for 3 months  for grazing . If the rent of the pasture is Rs. 175/-, how much must C pay as his share of rent? 

(a) Rs. 45

(b) Rs. 50

(c) Rs. 55

(d) Rs. 60

4.A, B, and C started a business with their investments in the ratio  1 : 2: 4. After 6 months A increased his capital by 50% and B invested twice the amount as before while C withdraw 1/4 of his own investment. The ratio of their profits at the end of the year was 

(a) 10 : 5 : 9 

(b) 5 : 12 : 14 

(c) 6 : 9 : 17 

(d) 5 : 14 : 16 

5.A starts business with Rs. 3500/- and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B’s contribution in the capital? 

(a) Rs. 8000 

(b) Rs. 8500 

(c) Rs. 9000 

(d) Rs. 7500

6.A number is divided into two parts in such a way that 80% of 1st part is 3 more than 60% of 2nd part and 80% of 2nd part is 6 more than 90% of the 1st part. Then the number is.

(a) 125  

(b) 130  

(c) 135  

(d) 145

7.A. B and C enter into a partnership. A invests Rs. 2400 for 4 years, B Rs. 2800 for 8 years and C Rs. 2000 for 10 years. They earn Rs. 1 170. Find the share of each.

(1) Rs. 420 

(2) Rs 540

(3) Rs. 108 

(4) Rs. 216

8.A, B and C enter into partnership with capital contribution of Rs. 25,000, Rs. 30,000 and Rs.15,000 respectively. A is the working partner and he gets 30% of the profit for managing the business. The balance profit is distributed in proportion to the capital investment. At the year-end, A gets Rs. 200 more than Band C together. Find the total profit.

(1) Rs. 2500 

(2) Rs. 2000

(3) Rs. 2200 

(4) Rs. 9.400

9.A, B and C enter into a partner ship. Their capital contribution is in the ratio 21 : 18 : 14. At the end of the business term they share profits in the ratio 15 : 8 :9. Find the ratio of time for which they invest their capitals.

(1)37 : 38 : 72

(2) 39 : 38 : 72

(3) 90 : 56 : 81

(4) None of these

10.A, B and C enter into a partnership. Their contributions are Rs.30 lakhs, Rs. 20 lakhs, and Rs.10 lakhs respectively. A and B are working partner while C is a sleeping partner. A and B get 10% and 15% of gross profit respectively as salary for managing the business. If at the year end C receives Rs. 3.75 lakhs,as profit, find the share of A.

(1) Rs. l6 Lakhs

(2) Rs. 12 Lakhs

(3) Rs. 18 Lakhs

(4) Rs. 20 Lakhs

ANSWERS AND SOLUTION
1.(b) 8A = B * 12 = 6C
=> 8A/24 = 12B/24 = 6C/24
=> A/3 = B/2 = C/4
so A : B : C  = 3 : 2 : 4
so B's share = 2/(3 + 2 + 4) * 864
= 2/9 * 864 = Rs. 192

2.(a) Initial investment :
A = Rs. 5x
B= Rs. 4x
C = Rs. 3x
so Ratio of their equivalent capitals for 1 month
= 5x * 12 : (4x * 4 + (4x + 1000) * 8) : (3x 8 + (3x + 2000) * 4)
= 15x : (12x + 2000) : 9x + 2000)
so 15x/(12x + 2000) = 15/14
=> 14x = 12x + 2000
=> 2x = 2000
x = Rs. 1000

3.(a) Share of rent = (number of oxen * time)
A : B : C
= (10 * 7) : (12 * 5) : (15 * 30)
A : B : C = 70 : 60 : 45
A : B : C = 14 : 12 : 9
C’s share of rent
= 9/(14 + 12 + 9) * 175
= 9/35 * 175 = 45
so C’s share of rent is Rs. 45

4.(b) Ratio of equivalent capital of A, B and C for 1 month
= (x * 6 + 3x/2 * 6) : (2x * 6 + 4x * 6) : (4x * 6 + 3x * 6)
= 15x : 36x : 42x
= 5 : 12 : 14

5.(c) A’s investment of Rs. 3500 is for 12 months
B’s investment (let it be Rs. x) is for 7 months only.
At the end of the year the profit is divided in the ratio 2 : 3 and
it must be equal to the ratio of the product. (Amount x time)
12 * 3500/ 7x = 2/3
Or, x = 12 * 3500/7 *  3/2
Or. X = 9000

6.(c)
7.(d) This is a case of compound partnership.
Rs. 2400 investment for 4 years earns as much as Rs. 2400 * 4 = Rs. 9600 in 1 year
Similarly, Rs. 2800 for 8 years is equivalent to Rs. 2800 * 8 = Rs. 22400 in 1 year
Rs. 2000 for 10 year is equivalent to Rs. 2000 * 10 = Rs. 20,000 in 1 year
The profit is, therefore, divided in the ratio
Rs.9600: Rs.22400: Rs.20000
or 12 : 28 : 25
Sum of the ratio = 12 + 28 + 25 = 65
Rs. 1170/65 = Rs. 18
So, A’s share = 12 * Rs. 18 = Rs. 216
8.(b)
9.(c) Ratio of profits = Ratio of capital multiplied by time.
so Ratio of time = Ratio of profits divided by respective capitals.
= 15/21 : 8/18 : 9/14
= 5/7 : 4/9 : 9/14 = 90/126 : 56/126 : 81/126
[126 is LCM of 7, 9 and 14]
A : B : C = 90 : 56 : 81.
10.(c)
 

10th
A:B:C=3:2:1
A:B:C=10%+37.5%:15%+25%:12.5%= 47.5:40:12.5
C's share 12.5%=3.75
1%=3.75/12.5=0.3
A's share = 47.5*0.3=14.25 lac