Zoho Ratio and Proportion Quiz 1

x : y = 1 : 4 means x/y = 1/4

 

Now, (4x + y) : (2x + 3y) = (4x + y) / (2x + 3y) [Divide numerator and denominator by y.]

= \frac{\frac{4x +y}{y}}{\frac{2x+3y}{y}}

 

= [4(\frac{x}{y}) + 1]/[2(\frac{x}{y}) + 3], put \frac{x}{y} = \frac{1}{4}

 

We get = [4(\frac{1}{4}) + 1]/[2(\frac{1}{4}) + 3]= (2)/ ( ½ + 3 ) = \frac{4}{7}

Therefore the value of (4x + y) : (2x + 3y) 

 = 4 : 7

Let the number of 10 p, 50 p and 25 p coins be 5x, 1x and 2x 

 

Then 5x \times(\frac{10}{100})+1x \times(\frac{50}{100})+2x \times(\frac{25}{100}) = 276

 

\frac{x}{2}+\frac{x}{2}+\frac{x}{2}=276

 

\frac{3x}{2} = 276

 

3x = 276\times2

 

3x = 552

 

x = 552/ 3 = 184

 

Number of coins of 25 p type coin = 2x = 2*184 = 368

Let 5A = 10B = 2C = x

 

So, A = x/5 B = x/10 C = x/2

 

The L.C.M of 5, 10 and 2 is 10

 

Therefore, A : B : C = \frac{x}{5} * 10 : \frac{x}{10}* 10 : \frac{x}{2} \times 10 = 2x: x: 5x

 

= 2 : 1 : 5

 

Therefore, A : B : C = 2 : 1 : 5

Let the number to be added be x, then (1 + x) : (4 + x) = 3 : 5

 

\frac{1+x}{4+x} = 3/5

 

5(1 + x) = 3(4 + x)

 

5 + 5x = 12 + 3x

 

5x - 3x = 12 - 5

 

2x = 7

 x =  \frac{7}{2}

Length of ribbon originally = 50 cm

 

Let the original length be 10x and the reduced length be 7x.

 

But 10x = 50 cm

 

x = 50/10 cm = 5 cm

 

Therefore, reduced length = 7x 

 

= 7 * 5 cm = 35 cm 

Let the money received by Reshma, Sumita, and Megha be 2x, 7x, and x respectively.

 

Given that Megha has got Rs 257.

 

Therefore, x = 257

 

So, Reshma got = 2x

 

                   = Rs 2 * 257 = Rs 514

 

Sumita got = 7x

 

              = 7 * 257 = Rs 1799

Therefore, the total amount received by Reshma and Sumita is Rs (514 + 1799) = Rs 2313

Let the fourth term be x.

 

Thus 13, 24, 52, x are in proportion.

 

Product of extreme terms = 13 * x

 

Product of mean terms = 24 * 52

 

Since, the numbers make up a proportion

 

Therefore, 13x = 24 * 52

 

Or x = \frac{24*52}{13}

 

or, x = 96

 

Therefore, the fourth term of the proportion is 96.

Sol: Number of girls in the class = 48

 

Ratio of boys and girls = 3 : 1

 

According to the question,

 

Boys/Girls = 3/1

 

Boys/48 = 3/1

 

Boys = \frac{48\times 3}{1} = 144

 

Therefore, total number of students = 144 + 48 = 192

Let the third proportional of 4 and 60 be x.

 

Then 4, 60, x are in proportion.

 

This means 4 : 60 = 60 : x

 

So, 4 x = 60 * 60

 

x = 3600/4 = 900

 

Therefore, the third proportional of 4 and 60 is 900.

 Total number of people = 1536 + 1280 = 2816

Women : total number of people = 1280/2816 = 5:11

So, ratio of women to the number of people = 5:11