## WBCS MAIN PAPER VI : MATHEMATICS - RATIO PROPORTION MIXTURE ALLEGATION

- WBCS Main Examination Paper - VI : 2021
- WBCS Main Examination Paper - VI : 2020
- WBCS Main Examination Paper - VI : 2019
- WBCS Main Examination Paper - VI : 2018
- WBCS Main Examination Paper - VI : 2017
- WBCS Main Examination Paper - VI : 2016
- WBCS Main Examination Paper - VI : 2015
- WBCS Main Examination Paper - VI : 2014

1.The ratio of cost price to sale price is 20:23. What is the profit percentage? (A) 20%** (B) 15% **(C) 5% (0) 6%

2.A trader mixes three varieties of groundnuts costing Rs.50, Rs.20 and Rs.30 per kg in the ratio 2:4:3 in terms of weight and sells the mature at Rs.33 per kg. What percentage of profit does he make?

(A) 8% (8)9% **(C) 10% **(D) None of the above

3.A milkman has 21 litres of whole milk, 42 litres of toned milk and 63 litres of double toned milk. If he wants to pack the three types of milk in cans so that in no can two types of milk are mixed, then what is the minimum number of can would he require?

(A) 12 (8)** (C) 6 **(0) 3

4.Which of the following ratios is greatest?

(A) 7:15 (6) 15:23 (C) 17:25 (**D) 21:29**

1.Gold and Copper are heavier than water by 19 and 9 times respectively. In what proportion should they be mixed to form an alloy so that it will be heavier than water by 15 times ?

(A) 1 : 2 (B) 2 : 3 (C) 3 : 4 **(D) 3 : 2**

2.Mohit went to a shop to buy 50 kg of rice. He buys two varieties of rice which cost him Rs. 4.50 per kg and Rs. 5 per kg. He spends a total of Rs. 240. What was the quantity of less expensive rice bought by him ?

**(A) 20 kg** (B) 25 kg (C) 30 kg (D) 35 kg

3.The ratio of syrup and water in 30 litre of a mixture is 1 : 5, then the amount of water required to mix to make the ratio 1 : 6 is

(A) 3 litres (B) 4 litres **(C) 5 litres** (D) 6 litres

4.While preparing mixture of tea, 5% tea is lost. In what ratio a trader should mix two kinds of tea costing Rs. 600/kg and Rs. 450/kg respectively so that he might gain 25% on selling the mixed tea at Rs. 625/kg ?

(A) 3 : 5 (B) 4 : 5 (C) 5 : 2 **(D) 1 : 5**

5.Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is

(A) 9 (B) 11 (C) 13 **(D) 15**

6.If the current ratio of the father's age to the son's age is 4 : 1 and the product is 256, what will be the ratio of ages after 5 years ?

**(A) 37 : 13** (B) 38 : 12 (C) 35 : 15 (D) 50 : 1

7.Suppose milk is sold at the rates of 5.50, 6.00, 5.75 and 5.25 rupees per litre in four different months. Assuming that equal amount of money are spent on milk by a family in the four months, the average price in rupees per litre will be

**(A) 5.61** (B) 5.62 (C) 5.63 (D) 5.64

8.The ratio of the no. of white balls in a bag to that of black balls is 1 : 2. If 9 grey balls are added the ratio of nos. of white, black and grey becomes 2 : 4 : 3. How many black balls were in the bag ?

(A) 6 (B) 9 **(C) 12** (D) 8

9.A pipe can fill a tank in 16 hours. Due to a leak in the bottom, it's filled in 24 hours. If the tank is full, how much time will the leak take to empty it ?

(A) 36 hours (B) 42 hours (C) 45 hours **(D) 48 hours**

10.A man buys milk at Rs. 60 per litre, adds water to it and then sells it at Rs. 50 per litre. What is the ratio of milk and water if his profit in the deal is 20% ?

(A) 5 : 9 **(B) 25 : 11** (C) 16 : 19 (D) 13 : 16

11.If the first and second of the five numbers in continued proportion are 2 and 8 respectively, then the fifth number is

**(A) 512** (B) 16 (C) 64 (D) 256

12.Barun invests Rs. 5000 for a year and Tarun joins him with Rs. 8000 after six months. After the year they receive a return of Rs. 4500, then Tarun's share is

**(A) Rs. 2000** (B) Rs. 2500 (C) Rs. 2200 (D) None of the above

1.The ratio of bus and train fares from Burdwan to a certain place is 3 : 4. If the train fare increases by 20% and bus fare by 10% then what will be the new ratio of bus and train fares ?

(A) 12 : 23 **(B) 11 : 16** (C) 12 : 15 (D) 16 : 15

2.A laboratory has to pay Rs.67.50 for 30 days as gas bill. If it uses 35 gas burners for 6 hours a day. Find the amount to be paid if it uses 30 gas burners for 18 days working 7 hours a day.

**(A) Rs.40.50** (B) Rs.42.50 (C) Rs.44.50 (D) Rs.50.50

3.In what ratio should the Assam tea at Rs.40 per kg and Darjeeling tea at Rs.65 per kg be mixed and sold at Rs.60 per kg to make in overall profit of 25% ?

(A) 1 : 2 (B) 2 : 1 (C) 3 : 2 **(D) 17 : 8**

4.A milkman mixed water with 60 litres of pure milk and sold the mixture at the cost price thereby made a profit of 25%. Find the quantity of water in the mixture.

(A) 12 litres **(B) 15 litres** (C) 10 litres (D) 14 litres

5.Two friends start a business with the capitals Rs.16,000 and Rs.24,000. They make a profit of Rs.3375 in a year. How much each friend will get as a part of the profit ?

**(A) Rs.1350, Rs.2025** (B) Rs.1525, Rs.2225 (C) Rs. 1025, Rs.1850 (D) Rs.1250, Rs.2225

6.Mr. X invests Rs.600 for 5 months and Y invests Rs.500 for 9 months in a business. The part of the profit will be distributed among them in the ratio.

(A) 3 : 2 (B) 4 : 3 (C) 6 : 5 **(D) 2 : 3**

7.In a partnership business the total profit of A and B is Rs.2000. If the capital of A is Rs.6000 and profit is Rs.1200, then the capital of B is

**(A) Rs.4000 ** (B) Rs.5000 (C) Rs.4500 (D) Rs.3000

8.In a joint business X invests Rs.6000 for 9 months and Y invests Rs.8000 in some months. They get Rs.1800 and Rs.1600 as profit. In the business, the investment of Y was for

(A) 4 months (B) 5 mooths **(C) 6 months** (D) 8 months

9.In a joint business the capitals of A and B are in the ratio 3 : 4 and the capitals of B and C are in the ratio 6 : 5. If A gets a profit of Rs.450, find the profit of C.

(A) Rs.400 **(B) Rs.500 **(C) Rs.600 (D) Rs.450

10.In a joint business the capitals of P, O and R are in the ratio 1/4:1/3:1/2. At the end of the year they make a profit of Rs.3900. Find how much of the profit C will get

(A) Rs.2000 (B) Rs.1500 (C) Rs.1200 **(D) Rs.1800**

11.Three friends *P, Q* and *R* started a business with the capitals Rs.15,000, Rs.10,000 and Rs.25,000. But at the end of the year, they suffer a loss of Rs.25,000. How much each will have to pay for the loss ?

(A) Rs. 500, Rs. 750 and Rs. 1000

**(B) Rs. 750, Rs. 500 **and** Rs. 1250**

(C) Rs. 500, Rs. 750 and Rs. 1150

(D) Rs. 1000, Rs. 500 and Rs. 700

12.At the starting of the year *X* and *Y* jointly start a business with Rs.24,000 and Rs.30,000. After 5 months A invests Rs. 12,000 more in the business. At the end of the year if the profit in the business is Rs.14,030, find the part of the profit of each of them.

(A) Rs.8130, Rs.5900 (B) Rs.9130, Rs.4900 **(C) Rs.7130, Rs.6900** (D) Rs. 6130, Rs.7900

13.X and Y Jointly start a business with Rs.1200 and Rs.800. At the end of the year Y gets Rs,120 as profit. As a part of profit X will get

(A) Rs.200 **(B) Rs.180** (C) Rs.175 (D) Rs.150

14.X, Y and Z start a business with Rs.7200. After 1 year X, Y and Z get Rs.60, Rs.90 and Rs.120 as profit. Z invests an amount

(A) Rs.1800 (B) Rs.2400 (C) Rs.2700 **(D) Rs.3200**

15.In a business P invests Rs.12,000. After some days Q joins the business and invests Rs.16,000 in it. 9 months after Q joins, P and Q get same profit. Find for how many months P's money was invested in the business.

(A) 20 months (B) 11 months **(C) 12 months** (D) 10 months

16.P starts a business with capital of Rs.5000. After 3 months Q joins in the business with capital Rs.6000 and after 5 months R invests Rs.8000 in the business. At the end of the year of the profit is Rs.3400, how much money each will get ?

**(A) Rs. 1200, Rs.l080 **and **Rs.1120**

(B) Rs.1200, Rs.1100 and Rs.1000

(C) Rs.1200, Rs.1000 and Rs.800

(D) Rs.1200, Rs.900 and Rs.1100

17.S and T start a business with Rs.2400 and Rs.1600. After one year if S suffers a loss of Rs.45 in the business, then loss of T is

(A) Rs.25 **(B) Rs.30 **(C) Rs.32 (D) Rs.42

18.P and Q are partners sharing profits in the ratio of 3 : 2. P surrenders 1/6th of his share and Q surrenders 1/4th of his share in favour of R, a new partner. What is the sacrificing ratio ?

(A) 3 : 2 (B) 2 : 3 **(C) 1 : 1** (D) 3 : 11

19.S and T are partners sharing profits in the ratio of 3 : 2. W admitted as a partner. The new profit sharing ratio of S, T and W is 4 : 3 : 2. Find out the sacrificing ratio.

(A) 3 : 5 **(B) 7 : 3** (C) 5 : 3 (D) 3 : 7

20.P and Q were partners sharing profits in the ratio of 3 : 2. They admit R and S as new partners. P surrenders 1/3rd of his share in favour of R and Q surrenders 1/4th of his share in favour of S. Calculate the new profit sharing ratio of P, Q, R and S.

**(A) 4 : 3 : 2 : 1 **(B) 5 : 4 : 3 : 2 (C) 4 : 4 : 3 : 2 (D) 4 : 4 : 3 : 1

21.A and B are partners sharing profits in the ratio of 7 : 5. They agree to admit C, their manager into partnership, who is to get 1/6th share in profits. He acquires his share 1/24th from A and

1/8th from B. Calculate the new profit sharing ratio.

(A) 13 : 11 : 9 **(B) 13 : 7 : 4 **(C) 13 : 11 : 7 (D) 13 : 11 : 5

22.A, B and C are partners in a firm sharing profits in the ratio of 4 : 3 : 2. They admit D as a new partner. A, B and C each surrendered 1/3rd of their shares in favour of D. Calculate the new profit sharing ratio of A, B, C and D.

**(A) 8 : 6 : 4 : 9** (B) 8 : 6 : 5 : 4 (C) 8 : 7 : 6 : 9 (D) 8 : 6 : 7 : 9

23.A and B are in partnership sharing profits and losses in the ratio of 3 : 2. They admit C as a new partner. Calculate the new profit sharing ratio if C purchases 1/10th share from A.

(A) 5 : 4 : 3 (B) 4 : 3 : 2 (C) 3 : 2 : 1 **(D) 5 : 4 : 1**

24.A and B are partners in a firm sharing profits and losses in the ratio of 5 : 3. They admit C as a partner for 1/4th share in the profits of the firm. Calculate the new profit sharing rato of A, B and C if C acquires his share 1/5th from A and 1/20th from B.

(A) 17 : 15 : 13 **(B) 17 : 13 : 10 **(C) 17 : 13 : 11 (D) 17 :.15 : 10

25.P and Q start a joint business. P invests Rs.500 for 9 months and Q invests some money in the business for 6 months. The total profit in the business is Rs.69 and Q gets a profit of Rs.46. The capital of Q in the business is

**(A) Rs.1500** (B) Rs.3000 (C) Rs.4500 (D) Rs.6000

26.In a joint business the ratio of the capitals of three partners is 5 : 7 : 9. If the profit in the business is Rs.420, then the third partner will get

(A) Rs.100 (B) Rs.140 **(C) Rs.180** (D) Rs.200

27.A and B are equal partners. They admit C and D as partners with 1/5th and 1/6th share respectively. What is the profit sharing ratio of all the partners ?

**(A) 19 : 19 : 12 : 10** (B) 21 : 19 : 13 : 9 (C) 19 : 17 : 13 : 10 (D) 19 : 17 : 15 : 11 .

28.A and B are partners sharing profits in the ratio of 7 : 3. They admit C for

1/5th share, which he acquires in equal proportions from both. Find the new profit sharing ratio

(A) 2 : 1 : 1 (B) 3 : 2 : 1 (C) 4 : 3 : 1 **(D) 3 : 1 : 1**

29.A and B are partners sharing profits in the ratio of 5 : 4. they admit C for

1/9th share, which he acquires from A. Find out the new profit sharing ratio.

(A) 3 : 3 : 1 (B) 2 : 2 : 1 **(C) 4 : 4 : 1** (D) 5 : 5 : 2

30.X and Y are partners in a firm sharing profits in the ratio of 3 : 2. They admit R as a new partner from 1st April, 2019. X gives 1/3rd of his share while Y gives 1/10th from his share. Calculate the sacrificing ratio.

(A) 3 : 2 (B) 2 : 1 (C) 2 : 3 **(D) 1 : 2**

31.A waiter's income consists of his salary and tips. During one week his tips were 5/4 of his salary, What fraction of his income came from tips ?

(A) 4/9 (B) 5/4 (C) ⅝ **(D) **5/9

1.The ratio of Velocity of hour's hand and minute's hand at a clock is

**(A) 1 : 12** (B) 12 : 1 (C) 1 : 24 (D) 24 : 1

2.The Length of radius of spherical gas balloon increases from 7 cm to 21 cm as air being pumped into it. The ratio of surface areas of the balloon in two cases is

(A) 9 : 1 (B) 49 : 21 **(C) 1 : 9** (D) 7 : 441

3.A trader mixes three varieties of groundnuts costing Rs. 50, Rs. 20 and Rs. 30 per kg. in the ratio 2 : 4 : 3 in terms of weight and sells the mixture at Rs. 33 per kg. What percentage of profit does he make ?

(A) 8% (B) 9% **(C) 10%** (D) None of the above

4.Which of the following ratios is greatest ?

(A) 7 : 15 (B) 15 : 23 (C) 17 : 25 **(D) 21 : 29**

5.Present age of Neha and Rashmi are in the ratio of 7 : 8 respectively. Six years hence, the ratio of their ages will become 9 : 10 respectively. What is Rashmi's present age ?

(A) 36 **(B) 24** (C) 28 (D) 40

6.A circular copper wire of radius 7 cm is bent to form a rectangle. If breadth and length of the rectangle are in the ratio of 4 : 7 respectively, what is the breadth of the rectangle ? (in cm.)

**(A) 8 cm**. (B) 14 cm. (C) 10 cm. (D) 12 cm.

7.A man saved Rs. 16,500 in 10 years. In each year after the first year he saved Rs. 100 more than he did in the preceding year. How much did he save in the first year ?

**(A) Rs.1200** (B) Rs.1650 (C) Rs.1000 (D) Rs.1020

1.A mixture of 40 litres of milk and water contains 10% water. How much water should be added to this mixture so that the new mixture contains 20% water ?

(A) 6.5 litres **(B) 4 litres** (C) 5 litres (D) 7.5 litres

2.If a : b = c : d = e : f = 1 : 2, then (3a + 5c +7e) : (3b + 5d +7f) = ?

**(A) 1 : 2** (B) 1 : 4 (C) 2 : 1 (D) 8 : 7

3.The ratio of cost price and selling price of an article is 20 : 21. What is the profit per cent on it ?

(A) 5.5% **(B) 5%** (C) 6% (D) 6.25%

4.On dividing a sum of Rs. 832 between A and B in the ratio ⅕ : ⅕ , their shares are

(A) Rs. 500, Rs. 332 (B) Rs. 530, Rs. 302 **(C) Rs. 520, Rs. 312** (D) Rs. 490, Rs. 342

5.In a mixture of 60 litres, the ratio of milk and water is 2 :1. If the ratio of milk and water is to be 1 : 2, then the amount of water (in litres) to be further added is

(A) 30 (B) 20 (C) 40 **(D) 60**

6.If 2x = 3y = 4z, then x : y : z is

(A) 4 : 3 : 2 **(B) 6 : 4 : 3** (C) 6 : 3 : 2 (D) 3 : 4 : 2

7.If 20% of (p + q) = 50% of (p - q), then p : q = ?

**(A) 7 : 3** (B) 5 : 7 (C) 7 : 5 (D) 7 : 8

1.If P = 50% of Q and Q = 50% of R, then P : Q : R = ?

**(A) 1 : 2 : 4** (B) 1 : 4 : 2 (C) 4 : 2 : 1 (D) 2 : 1 : 4

2.In what ratio must water be mixed with milk to gain 16 ⅔ % on selling the mixture at cost price ?

**(A) 1 : 6** (B) 2 : 3 (C) 4 : 3 (D) 6 : 1

3.The diagonals of two squares are in the ratio 5 : 2. The ratio of their areas is -

**(A.) 5 : 2** (B) 25 : 4 (C) 125 : 8 (D) 4 : 25

4.The value of ¾ of a property is Rs, 21,000, the value of 4/7 of the same property is-

**(A) Rs. 16,000** (B) Rs. 28,000 (C) Rs. 14,000 (D) Rs. 19,000

5.Two numbers are in the ratio of 3 : 5. If each number is increased by 10, the ratio becomes 5 : 7. The numbers are -

(A) 3, 5 (B) 7, 9 (C) 13, 22 **(D) 15, 25**

6.The ratio of two numbers is 5 : 8 and their difference is 69. Then the two numbers are -

(A) 69, 128 **(B) 115, 184** (C) 43, 112 (D) 128, 197

7.If the sides of a triangle are in the ratio 3 : 4 : 5, then the largest angle is -

(A) 50° **(B) 75°** (C) 90° (D) 120°

8.If a : b = 3 : 4, then (7a + 3b) : (7a - 3b) = ?

(A) 4 : 3 (B) 5 : 2 **(C) 11 : 3** (D) 37 : 19

9.Gold is 19 times as heavy as water and copper is 9 times as heavy as water. The ratio in which these two metals be mixed so that the mixture is 15 times as heavy as water, is —

(A) 1 : 2 (B) 2 : 3 **(C) 3 : 2** (D) 19 : 135

10.Mean proportional to 0.32 and 0.02 is -

(A) 0.8 **(B) 0.08** (C) 0.008 (D) 0.4

11.If 2A = 3B = 4C, then A : B : C is -

(A) 2 : 3 : 4 (B) 4 : 3 : 2 **(C) 6 : 4 : 3** (D) 3 : 4 : 5

12.In a school, the ratio of boys and girls is 4 : 5. When 100 girls leave the school, the ratio becomes 6 : 7. How many boys are there in the school ?

(A) 1300 (B) 1500 (C) 1600 **(D) 1200**

13.Two whole numbers whose sum is 64, cannot be in the ratio -

(A) 5 : 3 (B) 7 : 1 **(C) 3 : 4** (D) 9 : 7

14.A, B, C is started a shop by investing Rs. 27,000, Rs. 81,000 and Rs. 72,000 respectively. At the end of one year, B's share of total profit was Rs. 36,000. The total profit was -

(A) Rs. 1,08,000 (B) Rs. 1,16,000 **(C) Rs. 80,000** (D) Rs. 92,000

15.Rs. 6,400 are divided among three workers in the ratio 3/5:2:5/3. The share of the second worker is-

(A) Rs. 2,560 **(B) Rs. 3,000** (C) Rs. 3,200 (D) Rs. 3,840

16.In what proportion must water be added to spirit to gain 20% by selling it at the cost price ?

(A) 2 : 5 **(B) 1 : 5** (C) 3 : 5 (D) 4 : 5

17.The perimeter of a rectangle and a square is same, i.e. 80 metres. But length and breadth of the rectangle is in the ratio 3 : 5. The ratio of area of rectangle : square is -

(A) 3 : 5 (B) 9 : 25 (C) 16 : 15 **(D) 15 : 16**

1.Speeds of a motorbike and a scooter are in the ratio 7 : 4. If the motor bike takes 4 hours to go 140 km., time taken by the scooter to go 60 km. is

(A) 2hrs. (B) 2 ½ hrs. **(C) 3 hrs.** (D) 3 ½ hrs.

2.Three numbers are in the ratio 3 : 4 : 5. The sum of the largest and the smallest equals the sum of the third and 52. The smallest numbei is

(A) 20 (B) 27 (C) 39 **(D) 52**

3.If ab = 36, then which of the following is correct ?

**(A) a : 9 = 4 : b** (B) 9 : a = 4 : b (C) a : 18 = b : 3 (D) a : 6 = b : 6

4.A TV and a VCR together cost Rs. 35000. If TV is 1.5 times costlier than VCR, find the cost of VCR.

(A) Rs. 13000 **(B) Rs. 14000** (C) Rs. 15000 (D) Rs. 16000

5.If a : b = b : c, then a4 : b4 = ?

(A) b2 : ac **(B) a****2**** : c****2**** **(C) c2 : a2 (D) ac : b2

6.If a : b = c : d = e : f = 1 : 2, then (3a + 5c + 7e) : (3b + 5d +7f) = ?

**(A) 1 : 2** (B) 1 : 4 (C) 2 : 1 (D) 8 : 7

7.The ratio in which two types of tea one Rs. 300 per kg. and other Rs. 175 per kg. be mixed and sold for Rs. 250 per kg. to make a profit of 25% is

(A) 1 : 2 **(B) 1 : 4** (C) 2 : 3 (D) 2 : 5

8.If A : B = B : C = C : D = 2 : 3 then A : B : C : D is

(A) 6 : 9 : 12 : 18 **(B) 8 : 12 : 18 : 27** (C) 10 : 15 : 16 : 24 (D) 12 : 18 : 27 : 36

9.In a mixture ratio of first and second liquid is 2 : 3 and in another mixture ratio of those two liquids is 5 : 4. Ratio in which the two mixtures be mixed so that quantity of two liquids in the new mixture be equal is

(A) 2 : 5 (B) 3 : 7 **(C) 5 : 9** (D) 9 : 11

10.A starts a business at the beginning of the year with a capital Rs. 9,000. After 3 months B Joined the business with a capital Rs. 12,000. If the profit at the end of 2 years be Rs. 9620 difference between the profit of A and B is

**(A) Rs. 740** (B) RS.750 (C) Rs. 760 (D) Rs. 770

11.If A : B : C = 2 : 3 : 4, then

(A) 8 : 9 : 16 (B) 8 : 9 : 12 **(C) 8 : 9 : 24** (D) 4 : 9 : 16

1.The ratio of bus and train fares from Kolkata to Burdwan is 3 : 4 . If the train fare increases by 20% and bus fare by 10% then what will be new ratio of bus and train fares ?

(A) 2 : 3 (B) 3 : 4 **(C) 11 : 16** (D) 13 : 20

2.The ratios of the quantities of first and second liquid in two mixtures are 2 : 3 and 5 : 4 respectively. In what ratio these two mixtures are to be mixed to have a new mixture of the two liquids with equal quantities ?

(A) 2 : 3 (B) 3 : 5 (C) 4 : 7 **(D) 5 : 9**

3.Two numbers are in the ratio 3 : 5. If each number is increased by 10, the ratio becomes 5 : 7. The sum of the numbers is -

(A) 8 (B) 16 (C) 35 **(D) 40**

4.If 2A = 3B = 4C then A : B : C is equal to

(A) 2 : 3 : 4 (B) 4 : 3 : 2 **(C) 6 : 4 : 3** (D) 3 : 4 : 6

5.The ratio between present age of X and Y is 5 : 3 respectively. The ratio between X's age 4 years ago and Y's age 4 years hence is 1 : 1. What will be the ratio between X's age 4 years hence and Y's 4 years ago ?

(A) 1 : 3 (B) 2 : 1 **(C) 3 : 1** (D) 4 : 1