Ratio and Proportion - Quiz

Let X be the income of A.
Then, the income of B is 4X.

The expenditure of A is 2X * 2/3 = 4/3X.
The expenditure of B is 4X * 3/3 = 4X.

We are given that the saving in each case is 200, so we can set up the following equations:
X - 4/3X = 200
4X - 4X = 400

Solving these equations gives us X = 200.

Substituting this value back into the equations for the income of A and B, we find that the income of A is 3 * 200 = 600 and the income of B is 4 * 200 = 800.

Therefore, the income of A is 600 and the income of B is 800.

Let the First-year income = 2x
And, Second-year income = 3x
But ATQ, the second-year income = 45000
So, x = 45000/3 = 15000
Then, first-year income = 2*15000=30000

Similarly,
Let the first-year expenditure = 5y
The first-year expenditure =25000
So, y = 25000/5 = 5000
Second-year expenditure = 9y= 9* 5000 = 45000

Apply formula:

Income = expenditure + savings
Or, savings = income - expenditure
Or, first-year savings = 30000- 25000 = 5000
Similarly,
Second-year savings = 45000- 45000 = 0

Now, total saving in two years = first-year savings + second-year savings
Or, Total saving = 5000+0 = 5000.

Here is the equation version of the solution:

First year income: 2x
First year expenditure: 5y
First year savings: 2x - 5y = 5000
Second year income: 3x
Second year expenditure: 9y
Second year savings: 3x - 9y = 0
Total saving: 5000 + 0 = 5000

Where x and y are variables representing the first year income and expenditure, respectively.

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

The ratio of land: water = 1: 2
In the northern hemisphere the ration of land: water = 2: 3

Note: Earth is divided equally into two hemispheres called northern hemisphere and southern hemisphere.

i.e., the northern hemisphere is 50% of the total earth.

We can say southern hemisphere = total area- northern hemisphere.

To make the northern hemisphere 50% of the total area
Multiply the ratio of the earth by 10 and northern hemisphere by 3
Now, earth's ratio Land: water = 1*10: 2*10 = 10: 20............... (i)
Northern hemisphere's ratio = 2*3: 3*3 = 6: 9...................... (ii)

Subtract equation i by ii

Hence, southern hemisphere = 10- 6: 20-9 = 4: 11

4/15 A = 2/5 B
=>A = (2/5 * 15/4) B
=>A = 3/2 B
=>A/B = 3/2
A : B = 3 : 2
Therefore B's share = Rs. (1210 * 2/5) = Rs. 484

 Let the third number be x
Then, first number = 120% of x = 120x/100 = 6x/5
Second number = 150% of x = 150x/100 = 3x/2
Ratio of first two numbers = 6x/5 : 3x/2 = 12x : 15x = 4 : 5

If X be the required number, then
(45 x X)1/2 = 3 x (5 x 22)1/2
45X = 9 x 110
X = 22

Let X’s income be 3k then Y’s income is 4k.
Let X’s expenditure be 4g then Y’s expenditure is 5g.
But 3k = 9/10 (5g) or k = 3/2g
X’s saving/Y’s saving = (3k - 4g)/(4k - 5g)
[3 (3 / 2g) - 4g]/[ 4(3 / 2g) - 5g] = 1/2
X’s saving : Y’s saving = 1 : 2

Let number of boys = x
Let number of girls = y
Therefore x/y = B and y/x = G
3(B + G) = 3[(x/y) + (y/x)] = 3[(x2 + y2)/xy] > 3If the boy-to-girl ratio in a class is B and the girl-to-boy ratio is G, then 3 (B + G) equals?

Given, y/(x - z) = (y + x)/z
yz = xy + x2- yz - xz .. (1)
Also (x/y) = (y/(x - z)) => x2 - xz = y2 .. (2)
Using (1) and (2), we get yz = xy - yz + y2
2yz = xy + y2
2z = x + y
Only option (c) satisfies the equation