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The sum of 5% of a number and 4% of the other number is 2/3 of the sum of 6% of the first number and 8% of the second. The ratio of the first number to the second is

A.

2:3

B.

3:2

C.

3:4

D.

4:3

Answer with explanation

Answer: Option DExplanation

Let the first number be x and second number be y.

Accoroding to the question,

[5% of x + 4% of y] = (2/3)[6% of x + 8% of y]

[(5/100)x + (4/100)y] = (2/3)[(6/100)x + (8/100)y]

(5x + 4y)/100 = (2/3)[(6x + 8y)/100]

15x + 12y = 12x + 16y

15x – 12x = 16y – 12y

3x = 4y

x/y = 4/3

Therefore required ratio = 4 : 3

Workspace

A purse contains 342 coins consisting of one rupees, 50 paise and 25 paise coins. If their values are in the ratio of 11 : 9 : 5 then find the number of 50 paise coins?

A.

180

B.

150

C.

162

D.

99

Answer with explanation

Answer: Option CExplanation

Let the value of one rupee, 50 paise and 25 paise be 11x, 9x, 5x respectively.

No. of 1 rupee coins = (11x / 1) =11x

No. of 50 paise coins = (9x / 0.5) = 18x

No. of 25 paise coins = (5x / 0.25) = 20x

11x + 18x + 9x = 342

38x = 342

x = 9

Therefore, no. of 1 rupee coins = 11 x 9 = 99 coins

No. of 50 paise coins = 18 x 9 = 162 coins

No. of 25 paise coins = 20 x 9 = 180 coins

Workspace

B is inversely proportional to the cube of A. If B=3, A=2. If B = 8/9. Find the value of A.

A.

2

B.

3

C.

4

D.

6

Answer with explanation

Answer: Option BExplanation

As per the question, B is inversely proportional to A^{3}

i.e., B α 1/A^{3}

Or, B =k/ A^{3}

Given that, B=3, A=2

So, 3 = k/ 8, or k=24

Given that, B = 8/9

So, 8/9 = 24/A^{3}

A^{3} = (9*24)/8 = 27

So, A = ^{3}√ 27 = 3

Workspace

In a bag, there are a certain number of toy-blocks with alphabets A, B, C and D written on them. The ratio of blocks A:B:C:D is in the ratio 4:7:3:1. If the number of ‘A’ blocks is 50 more than the number of ‘C’ blocks, what is the number of ‘B’ blocks?

A.

650

B.

480

C.

578

D.

350

Answer with explanation

Answer: Option DExplanation

Let the number of the blocks A,B,C,D be 4x, 7x, 3x and 1x respectively

=> 4x = 3x + 50

=> x = 50.

So the number of ‘B’ blocks is 7*50 = 350.

Workspace

The ratio of the first and second class fares between the two stations is 5 : 4 and the no. of passenger travelling by first and second class is 1 : 30 If Rs. 5000 is collected as total fare what is the amount collected from fist class passenge

A.

Rs. 250

B.

Rs. 200

C.

Rs. 150

D.

Rs. 300

Answer with explanation

Answer: Option BExplanation

Given:

Ratio of the first and second class fares = 5 : 4

Ratio of number of passenger travelling by first and second class = 1 : 30

Total fare = Rs. 5000

Let the first class fare and second class fare be 5X and 4X respectively.

And the number of passenger travelling by first and second class be Y and 30 Y respectively.

As per the question,

Total fare from first class + Total fare from second class = Total fare

(5X*Y ) + (4X*30Y) = 5000

5XY + 120XY = 5000

125XY = 5000

XY = 40

Therefore, amount collected from fist class passenger = 5XY = 5(40) = Rs. 200.

Workspace

A person covers the different distances by train, bus, and car in the ratio of 4: 3: 2. The ratio of the fair is 1: 2: 4 per km. The total expenditure as a fair is Rs 720. Find the total expenditure as fair on the train.

A.

140

B.

150

C.

160

D.

170

Answer with explanation

Answer: Option CExplanation

Distance covered in the ratio T: B: C = 4: 3: 2

Fair ratio per km. T: B: C = 1: 2: 4

So, the ratio of total fair T: B: C = 4: 6: 8

Sum of the ratio of total fair = 18

But ATQ, it is 720, so multiply 18 by 40.

Now, multiply each and every ratio with 40.

The total expenditure as fair on a train = 4*40=160

Workspace

A, B, C started a business with their investments in the ratio 1:3 :5. After 4 months, A invested the same amount as before and B as well as C withdraw half of their investments. The ratio of their profits at the end of the year is :

A.

1 : 2 : 3

B.

3 : 4 : 15

C.

3 : 5 : 10

D.

5 : 6 : 10

Answer with explanation

Answer: Option DExplanation

Let their initial investments be x, 3x and 5x respectively. Then,

A:B:C = (x*4+2x*8) : (3x*4+(3x/2)*8) : (5x*4+(5x/2)*8)

20x : 24x : 40x = 5 : 6 : 10

Workspace

A.

2:3

B.

3:4

C.

4:3

D.

3:2

Answer with explanation

Answer: Option CExplanation

Let the first number be x and the second number be y.

Accoroding to the question,

[5% of x + 4% of y] = (2/3)[6% of x + 8% of y]

[(5/100)x + (4/100)y] = (2/3)[(6/100)x + (8/100)y]

(5x + 4y)/100 = (2/3)[(6x + 8y)/100]

15x + 12y = 12x + 16y

15x – 12x = 16y – 12y

3x = 4y

x/y = 4/3

Therefore required ratio = 4 : 3.

Workspace

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