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A bag contains Rs. 1, Rs. 2 and Rs. 10 coins in the ratio 2 : 5 : 6. Total amount in the bag is equal to Rs. 360. The total number of Rs. 2, Rs. 10 and Rs. 1 coins respectively are

A.

5, 6, 2

B.

10, 30, 25

C.

10, 25, 30

D.

25, 30, 10

Answer with explanation

Answer: Option DExplanation

Let the number of coins of Rs. 1, Rs. 2 and Rs. 10 be 2x, 5x and 6x respectively.

Therefore, Rs. 1 amounts to 2x

Rs. 2 amounts to 10x

And Rs. 10 amounts to 60x

Since, the total amount is Rs. 360

2x + 10x + 60x = 360

72x = 360 => x = 5

Therefore,

Rs. 1 = 2x = 2 * 5 = 10

Rs. 2 = 10x = 10 * 5 = 50

Rs. 10 = 60x = 60 * 5 = 300

Total no. of Rs. 1 coins = 10/1 = 10

Total no. of Rs. 2 coins = 50/2 = 25

Total no. of Rs. 10 coins = 300/10 = 30

Workspace

A.

10:5:4

B.

10:18:5

C.

10:4:5

D.

20:10:36

Answer with explanation

Answer: Option DExplanation

Part of the tank A can fill in 1 hr = 1/12

Let B can fill the tank in x hrs, then according to the question,

1/x + 1/12 = 1/8

x = 24 hrs

Also let C can empty the filled tank in y hrs then according to the question,

1/y – 1/ 12 = 1/15

1/y = 9/60

y = 20/3 hrs

Ratio of efficiencies of A, B and C = 1/12 : 1/24 : 3/20 = 10:5:18 = 20:10:36

Workspace

A bucket contains 40% water and 60% milk. Bucket B contains 35% water and 40% milk and 25% another liquid L. liquids of bucket A and B are mixed in the ratio of 1:4. What is the ratio of water and milk in the newly formed mixture?

A.

5:3

B.

9:11

C.

11:9

D.

3:5

Answer with explanation

Answer: Option BExplanation

assume the quantity of bucket A is 100 litres

And the quantity of bucket B is 400 litres

For bucket A,

Water = 40 L, milk = 60 L, liquid L = 0 litre

For bucket B,

Water = 35 % of 400 =140 L, milk = 40 % of 400 = 160 L, liquid L =25 % of 400 = 100 L

Final mixture,

Water = 180 L, milk = 220, liquid L = 100 L

Ratio of water and milk in new mixture = 180/500 : 200/500

36% : 44%

Workspace

Two alloys A and B are made from zinc and copper by mixing them in the ratio of 6:9 and 7:11 respectively. If 40g of alloy A and 60g of alloy B are melted and mixed to form another alloy C, then what is the ratio of zinc and copper in the new alloy C?

A.

2:3

B.

59:91

C.

5:9

D.

59:90

Answer with explanation

Answer: Option BExplanation

for alloy A (40g),

Zinc : copper = 6:9

Zinc = 40 X 6/ (6+9) = 16g

Copper = 40 X 9 / (9+6) = 24g

For alloy B (60g),

Zinc : copper = 7:11

Zinc = 60 X 7/(7+11) = 70/3g

Copper = 60 X 11 / (7+11) = 110/3g

So, in alloy C,

Zinc = 16 + 70/3 = 118/3g

Copper = 24 + 110/3 = 182/3g

Therefore the required ratio = 118:182 = 59:91

Workspace

Alka, Sudha and Shailja had amounts in the ratio of 3:4:5 respectively. Each of them got an additional amount of Rs. 8,000 and the ratio of amounts became 4:5:6 respectively. What was the amount Shailja had originally ?

A.

Rs. 24000

B.

Rs. 30000

C.

Rs. 36000

D.

Rs. 40000

Answer with explanation

Answer: Option DExplanation

Let the amounts of Alka, Sudha and Shailja be 3x,4x and 5x respectively.

When 8000 is added, let their amounts be 4k,5k and 6k respectively.

3x + 8000=4k….(1)

4x + 8000=5k….(2)

5x + 8000=6k….(3)

On solving we get x=8000 and k=8000

Thus, Shailja’s amount=5 x 8000=Rs.40,000

Workspace

A cubical block of metal weighs 6 pounds. How much will another cube of the same metal weigh if its sides are twice as long?

A.

12

B.

36

C.

60

D.

48

Answer with explanation

Answer: Option DExplanation

Explanation:

If you double the sides of a cube, the ratio of the surface areas of the old and new cubes will be 1: 4. The ratio of the volumes of the old and new cubes will be 1: 8.

Weight is proportional to volume. So, If the first weighs 6 pounds, the second weighs 6×8 pounds =48.

Workspace

The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?

A.

10 : 11 : 20

B.

23 : 33 : 60

C.

3 : 3 : 10

D.

None of these

Answer with explanation

Answer: Option BExplanation

Workspace

Rs.1170 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?

A.

Rs.360

B.

Rs.540

C.

Rs.260

D.

Rs.270

Answer with explanation

Answer: Option BExplanation

A+B+C = 1170

4A = 3B = 2C = x

A:B:C = 1/4:1/3:1/2 = 3:4:6

6/13 * 1170 = Rs.540

Workspace

A and B together have Rs. 1210. If 4/15 of A’s amount is equal to 2/5 of B’s amount. How much amount B have?

A.

Rs 478

B.

Rs 470

C.

Rs 484

D.

Rs. 480

Answer with explanation

Answer: Option CExplanation

In this type of question, we will first try to calculate the ratio of two persons. Once we get ratio then we can easily get our answer. So let us solve this.

Workspace

If x varies as y then x^{2}+y^{2} varies as

A.

x-y

B.

x+y

C.

x^{2}-y^{2}

D.

None of these

Answer with explanation

Answer: Option DExplanation

Given,

x = y;

Or, x-y = 0;

Or, (x-y)^{2} = 0;

Or, x^{2}+y^{2}-2xy = 0;

Or, x^{2}+y^{2} = 2xy

It means that, x^{2}+y^{2} varies as xy.

Workspace

If three numbers in the ratio 3 : 2: 5 be such that the sum of their squares is 1862, the middle number will be

A.

2218

B.

10

C.

20

D.

14

Answer with explanation

Answer: Option DExplanation

Let the numbers be 3x, 2x and 5x.

Then,

9x + 4x + 25x =1862

⇒ 38x = 1862

⇒ x = 49 ⇒ x = 7.

middle number = 2x = 14

Workspace

The ratio of two numbers is 2:3 and the sum of their cubes is 945. The difference of number is?

A.

6

B.

4

C.

5

D.

3

Answer with explanation

Answer: Option DExplanation

Let us assume 2:3 as 2x : 3x

2x 3x

8x cube + 27x cube = 945

35x cube = 945

x cube = 27 => x = 3

Workspace

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