MCQ Questions for Class 6 Maths Ratio And Proportion Quiz 6

Find the reduced form of the ratio of the first quantity to second quantity.

$3$ years

$4$ months,

$5$ years

$8$ months.

0%
17:10
0%
10:17
0%
10:15
0%
15:10

Explanation

firstly year change into months

$1$ year =

$12$ months

$3$ years = 12x3 =

$36$ months

$5$ years = 12x5 =

$60$ months

Then reduced form are in ratio

$\begin{array}{l} \dfrac { { 3\, years\, \, 4\, months } }{ { 5years\, \, 8\, \, months } } \\ =\dfrac { { \left( { 36+4 } \right) \, \, months } }{ { \left( { 60+8 } \right) \, \, months } } \\ =\dfrac { { 40 } }{ { 68 } } \\ =\dfrac { { 10 } }{ { 17 } } =10:17 \end{array}$

Find the reduced form of the ratio of the first quantity to second quantity.

$5$ litres,

$2500$ ml.

0%
$1:2$
0%
$2:1$
0%
$1:3$
0%
$3:4$

Explanation

Reduced form of

$5$ liters and

$2500\text{ ml}$

in ratio

$[1$ liter

$= 1000\text{ ml},$ so

$5$ liters

$= 5000\text{ ml}]$

$=\dfrac{{5\,\text{liters}}}{{2500\text{ml}}}\,\,\,\,\,$

$=\dfrac{{5000}}{{2500}}\,\,\,\,\,$

$=\dfrac{2}{1} \implies 2:1$

The ratio of 40 minutes to 2.5 hours is:

0%
$4:17$
0%
$4:18$
0%
$4:13$
0%
$4:15$

Explanation

Given quantities are

$40\ minutes$ and

$2.5\ hours$ .

Hence, their ratio will be:

$\dfrac {40\ min}{2.5\ hr}$

We see that the units of the two quantities are not same.

Hence, using the relation

$1 \ hour=60\ minutes$ , we get:

$\dfrac {40\ min}{2.5\times 60\ min}=\dfrac {40}{150}$

$=\dfrac {40}{150}$

$\Rightarrow 4:15$

Hence, the required ratio is

$4:15$ .

A class consists of 32 boys and 18 girls then the ratio of number of boys to the total number of students in the class is_____

0%
16:25
0%
25:16
0%
9:25
0%
25:9

Explanation

We have,

Number of boys $=32$

Number of girls $=18$

Then,

Total students in class

$=32+18$

$=50$

The ratio of number of boys to students in class is

$=\dfrac{Boys}{Total\,students}$

$=\dfrac{32}{50}$

$=\dfrac{16}{25}$

$=16:25$

Hence, this is the answer.

The food stocks in a hostel are sufficient for 1200 students for 20 days . If 400 more students joined the hostel , the stocks just for ... days .

0%
12
0%
15
0%
18
0%
21

Explanation

Let food stock is sufficient for

$x$ days.

Given,

$M_{1}=1200$

$D_{1}=20$

$M_{2}=1200+400=1600$

$D_{2}=x$

Then, using

$M_{1}D_{1}=M_{2}D_{2}$

$1200\times 20 = 1600\times x$

$x=\dfrac{1200\times 20}{1600}$

$x=15$

Therefore, now the food stock is sufficient for

$15$ days.

The ratio of 8 books to 12 books is?

0%
$2:3$
0%
$5:2$
0%
$4:5$
0%
$5: 4$

Explanation

The ratio of 8 book to 12 book is=

$\dfrac{8}{12}=\dfrac{2}{3}=2:3$

If A, B, C divide Rs. 1200 in the ratio 2 : 3 : 5, then B's share is

0%
Rs. 240
0%
Rs. 600
0%
Rs. 380
0%
Rs. 360

Explanation

Given that,
Total money =

$Rs. 1200$

$A: B: C = 2:3:5$
B's share =

$\cfrac{3}{(2 + 3 + 5)} \times 1200 = 360$

Mark the correct alternative of the following.
A ratio equivalent to

$2:3$ is

0%
$4 : 3$
0%
$2 : 6$
0%
$6 : 9$
0%
$10 : 9$

Explanation

Given the ratio is

$2:3$ .

Now,

$\dfrac{6}{9}$

$=\dfrac{2\times 3}{3\times 3}$

$=\dfrac{2}{3}$ .

So the equivalent ratio is

$6:9$ .

The ratio

$384 : 480$ in its simplest form is

0%
$3 : 5$
0%
$5 : 4$
0%
$4 : 5$
0%
$2 : 5$

Explanation

Given the ratio is

$384:480$

$=96\times 4: 96\times 5$

$=4:5$ .

If Rs.

$840$ is divided between

$P$ and

$Q$ in the ratio

$3:4$ , then P's share is

0%
Rs. $340$
0%
Rs. $480$
0%
Rs. $360$
0%
Rs. $400$

Explanation

Given

$P:Q=3:4$

Sum of ratio terms

$=3+4=7$

$\therefore P's$ share

$=\dfrac{3}{7}\times 840$

$=360$

Hence, option (C) is the correct answer

A ratio equivalent to

$2:5$ is

0%
$6:15$
0%
$4:5$
0%
$5:2$
0%
$5:4$

Explanation

The simplest form of ratio

$6 : 15 =2\times 3:5\times 3= 2 : 5$

So,

$2 : 5$ is equivalent to

$6 : 15$

Mark the correct answer in the following:
Choose the correct statement:

0%
$(5:8) > (3:4)$
0%
$(5:8) < (3:4)$
0%
two ratios cannot be compared
0%
None of the above

Explanation

We know that

$5:8=5/8$ and

$3:4=3/4$

To compare the ratios, we make their denominator same.

$\therefore 5:8=\dfrac 58$

And,

$3:4=\dfrac34=\dfrac68$ [Multiplying both numerator and denominator by

$2$ ]

Since,

$5<6$

$\Rightarrow \dfrac58<\dfrac68$

$\therefore (5:8) < (3:4)$

Hence, Option (B) is the correct answer.

In some situations, comparison of two quantities (of same kind) by difference does not make much sense.

0%
True
0%
False

The ratio of

$20$ minutes to

$1$ hour is

0%
$20:1$
0%
$1:3$
0%
$1:4$
0%
$2:5$

Mark the correct answer in the following:
If Rupees

$760$ is divided between

$A$ and

$B$ in the ratio

$8:11$ , then

$B's$ share is

0%
$Rupees\ 440$
0%
$Rupees\ 320$
0%
$Rupees\ 430$
0%
$Rupees\ 330$

Explanation

Given

$A:B=8:11$

Sum of ratio terms

$=8+11=19$

$\therefore B's$ share

$=\dfrac{11}{19}\times 760$

$=\cfrac{8360}{19}$

$=440$

Hence, option (A) is the correct answer

State whether the given statement is true (T) or false (F):

$20\ g:100\ g=1\ metre:500\ cm$

0%
True
0%
False

Explanation

Converting the ratios into same units and simplifying the ratios, we get

(i)

$20 \mathrm{~g}: 100 \mathrm{~g}=\frac{20 \mathrm{~g}}{100 \mathrm{~g}}=\frac{1}{5}$

(ii)

$1$ metre :

$500 \mathrm{~cm}=\frac{1 \text { metre }}{500 \mathrm{~cm}}=\frac{100 \mathrm{~cm}}{500 \mathrm{~cm}}=\frac{1}{5}$

After simplifying, both the ratios are the same, so the given ratios are equal.

$\therefore 20 \mathrm{~g}: 100 \mathrm{~g}=1 \text { metre }: 500 \mathrm{~cm}$

$\therefore \textbf{The given statement is True}$

State whether the given statement is true (T) or false (F):

$0.2:5=2:0.5$

0%
True
0%
False

Explanation

If two ratios are equal, ratios in its simplest fraction should also be equal
Simplifying the ratios, we get
(i)

$0.2: 5=\frac{0.2}{5}=\frac{2}{50}=\frac{1}{25}$
(ii)

$2: 0.5=\frac{2}{0.5}=\frac{20}{5}=4$

$\because \frac{1}{25} \neq 4$

$\therefore 0.2: 5 \neq 2: 0.5$

$\therefore \textbf{The given statement is false.}$

The greatest ratio among the ratios

$2:3$ ,

$5:8$ ,

$75:121$ and

$40:25$ is

0%
$2:3$
0%
$5:8$
0%
$75:121$
0%
$40:25$

Explanation

$\textbf{Step 1: Convert the fractions with same denominators.}$
Given ratios,

$2: 3=\frac{2}{3}$

$5: 8=\frac{5}{8}$

$75: 121=\frac{75}{121}$

$40: 25=\frac{40}{25}$
Finding the LCM of the denominators by prime factorisation, we get

$\begin{array}{l|l}2 & 3,8,121,25 \\\hline 2 & 3,4,121,25 \\\hline 2 & 3,2,121,25 \\\hline 3 & 3,1,121,25 \\\hline 5 & 1,1,121,25 \\\hline 5 & 1,1,121,5 \\\hline 11 & 1,1,121,1 \\\hline 11 & 1,1,11,1 \\\hline & 1,1,1,1 \\\hline\end{array}$

$\begin{aligned}\text {LCM of } 3,8,121,25=& 2 \times 2 \times 2 \times 3 \times 5 \times 5 \times 11 \times 11 \\&=72600\end{aligned}$
Converting the fractions with same denominators, we get

$\begin{aligned}&2: 3=\frac{2}{3}=\frac{2 \times 24200}{3 \times 24200}=\frac{48400}{72600} \\&5: 8=\frac{5}{8}=\frac{5 \times 9075}{8 \times 9075}=\frac{45375}{72600} \\&75: 121=\frac{75}{121}=\frac{75 \times 600}{121 \times 600}=\frac{45000}{72600} \\&40: 25=\frac{40}{25}=\frac{40 \times 2904}{25 \times 2904}=\frac{116160}{72600}\end{aligned}$

$\textbf{Step 2: Find the fraction with the greatest numerator.}$
Since all the denominators of the fractions are same, the fraction with the greatest numerator will be the greatest.

$\therefore \frac{116160}{72600}$ is the greatest fraction

$\Rightarrow 40: 25$ is the greatest ratio.

$\therefore \textbf{Option D is correct}$

State whether the given statement is true (T) or false (F):

$15\ m:40\ m=35\ m:65\ m$

0%
True
0%
False

Explanation

If two ratios are equal, ratios in its simplest fraction should also be equal

Simplifying the ratios, we get

(i)

$15 \mathrm{~m}: 40 \mathrm{~m}=\frac{15}{40}=\frac{3}{8}$

(ii)

$35 m: 65 m=\frac{35}{65}=\frac{7}{13}$

$\because \frac{3}{8} \neq \frac{7}{13}$

$\therefore 15 \mathrm{~m}: 40 \mathrm{~m} \neq 35 \mathrm{~m}: 65 \mathrm{~m}$

$\therefore \textbf{The given statement is false.}$

State whether the given statement is true (T) or false (F):

$4:7=20:35$

0%
True
0%
False

Explanation

If two ratios are equal, ratios in simplest fraction should be also be equal Simplifying the ratios, we get
(i)

$4: 7=\dfrac{4}{7}$
(ii)

$20: 35=\dfrac{20}{35}=\dfrac{20 \div 5}{35 \div 5}=\dfrac{4}{7}$
After simplifying, both the ratios resulted in

$\frac{4}{7}$

$\therefore 4: 7=20: 35$

$\therefore \textbf{The given statement is true.}$

There are

$b$ boys and

$g$ girls in a class. The ratio of the number of boys to the total number of students in the class is:

0%
$\dfrac{b}{b+g}$
0%
$\dfrac{g}{b+g}$
0%
$\dfrac{b}{g}$
0%
$\dfrac{b+g}{b}$

Explanation

Given number of boys in the class

$=b$
Number of girls in the class

$=g$
Total number of students in the class

$=b+g$

$\therefore$ Ratio of boys to total number of students

$=$ Number of boys: Total students

$\begin{aligned}&=b:(b+g) \\&=\frac{b}{b+g}\end{aligned}$

State whether the given statement is true (T) or false (F):

$12\ hours:30\ hours=8\ km:20\ km$

0%
True
0%
False

Explanation

Simplifying the ratios, we get

(i)

$12$ hours:

$30$ hours

$=\frac{12}{30}=\frac{2}{5}$

(ii)

$8 \mathrm{~km}: 20 \mathrm{~km}=\frac{8 \mathrm{~km}}{20 \mathrm{~km}}=\frac{2}{5}$

$\therefore 12$ hours:

$30$ hours

$=8 \mathrm{~km}: 20 \mathrm{~km}$

$\therefore \textbf{The given statement is True}$

State whether the given statement is true (T) or false (F):

$3:33=33:333$

0%
True
0%
False

Explanation

If two ratios are equal, ratios in its simplest fraction should also be equal Simplifying the ratios, we get
(i)

$3: 33=\frac{3}{33}=\frac{1}{11}$
(ii)

$33: 333=\frac{33}{333}=\frac{11}{111}$

$\because \frac{1}{11} \neq \frac{11}{111}$

$\therefore 3: 33 \neq 33: 333$

$\therefore \textbf{The given statement is false.}$

The model of a ship shown is of height 3.5 cm. The actual height of the ship is 210 cm if the scale chosen is 1:60.

0%
True
0%
False

Explanation

The given statement is true.
We know that,

Scale

$= \dfrac{shown\ height}{actual\ height}$

Given, shown height = 3.5 cm and actual height = 210 cm

Now, by putting the value in above formula

$=\dfrac{3.5}{210}=\dfrac{35}{2100}=\dfrac{1}{60}$

Hence, the ratio is 1 : 60.

$A$ ratio is always greater than

$1$ .

0%
True
0%
False

Explanation

False
A ratio can be less than

$1$ or greater than

$1$ or equal to

$1$
It is not necessary that it is always greater than

$1$ .

Ex:

$3:4 <1 \ ;\ 4:3>1\ ;\ 4:4=1$

State true or false :
A ratio of

$250\,gm$ and

$3 \,kg$ is

$1 : 12$

0%
True
0%
False

State true or false :
A ratio equivalent to

$7 : 9$ is

$27 : 21$

0%
True
0%
False

Explanation

Consider

$27:21$

$\cfrac{27}{21} =\cfrac{3 \times9}{3 \times7}=\cfrac{9}{7}$

The ratio of

$5:7$ is greater than the ratio

$5:6$ .

0%
True
0%
False

Explanation

The ratio of

$5:7$ is greater than the ratio

$5:6$ .
False
Explanation:

$\dfrac {5}{7}, \dfrac {5}{6}$

$\dfrac {30:35}{42}$

$30 < 35$

$5:7$ is not greater than the ratio

$5:6$

The ratio of

$75\ mL$ to

$3$ lires is

0%
$25:1$
0%
$40:1$
0%
$1:40$
0%
$3:200$

Explanation

$75\ ml$ to

$3$ litre

$=75:3000$

$=1:40$

State true or false :
A ratio equivalent to

5:45:4 is 240:192

0%
True
0%
False

CBSE Questions for Class 6 Maths Ratio And Proportion Quiz 6 - MCQExams.com

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CBSE Questions for Class 6 Maths Ratio And Proportion Quiz 6 - MCQExams.com

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