MATHS M.C.Q. [1 Marks Each]

The ratio $=2:\frac{1}{3}\rightarrow\frac{2}{1}=\frac{6}{1}$
or ratio $= 6 : 1$

Bus covers in $3$ hours $= 195\ km$
It will cover in $1$ hour $=\frac{195}{3}=65\text{km}$
Train cover in $4$ hours $=300\text{km}$
It will cover in $1$ hour $=\frac{300}{4}=75\text{km}$
$\therefore$ Ratio in thier speeds $=65:75$
$=13:15$

Given ratio $=\frac{1}{6}$
Now we add 4 to Antecedent or Numerator and $2$ to Consequentor Denominator as shown
$\Rightarrow\frac{1+4}{6+2}$
$\Rightarrow\frac{5}{8}$

Suppose,$\frac{\text{x}}{2\text{y}+\text{z}-\text{x}}=\frac{\text{y}}{2\text{z}+\text{x}-\text{y}}=\frac{\text{y}}{2\text{z}+\text{y}-\text{z}}=\frac{1}{\text{k}}$
$\Rightarrow\frac{\text{x}}{2\text{y }+\text{ z}-\text{x}}=\frac{1}{\text{k}},\frac{\text{y}}{2\text{z }+\text{ x}-\text{y}}=\frac{1}{\text{k}},\text{and }\frac{\text{y}}{2\text{z }+\text{ y}-\text{z}}=\frac{1}{\text{k}}$
$⟹ xk = 2y + z - x...................(1) yk = 2z + x - y .............. (2)$ and
$zk = 2x + y - z .............. (3)$ Adding $(1), (2)$ and $(3)$ we get $xk + yk + zk = 2x + 2y + 2z$
$⟹ (x + y + z) k = (x + y + z)$
$\therefore$ $k = 2$ Hence, each ratio is equal to $\frac{1}{2}$

The offfice hours are from $10.30\ AM$ to $5.30\ PM$ hence total office
hours are $7$ hours and lunch time hours is $\frac{1}{2}$ hours
ratio of office hrs to lunch time $=\frac{7}{\frac{1}{2}}$
this gives ratio $= 14 : 1$

$60$ hrs $= 60 \times 60$ mins $= 3600$ mins
Now, the ratio
$3600 : 600$
$= 6 : 1$

$10$ boys dig a patch in $= 12$ hours
$1$ boy will dig it in $= 12 \times 10$ hours
And $8$ boys will digit it in $\frac{12\times10}{8}$
$=15\text{ hours}.$

The ratio of $350g$ and $3\ kg$
first convert $3\ kg$ to $g$
we get $3g = 3000g$
$\text{ratio}=\frac{350}{3000}$
$\text{We getratio}=\frac{7}{60}$

Since, $1m = 100\ cm$
Required ratio $=\frac{5}{10}\times100=\frac{1}{200}$

$\text{largest}=\frac{90\times5}{1+3+5}$
$=\frac{90\times5}{9}$
$=50\text{cm}$

It is given that,
$\frac{\text{x}}{\text{y}}=\frac{1}{1}=1\ ....(1)$
Now,
$\frac{3\text{x}+4\text{y}}{5\text{x}+6\text{y}}=\frac{(3\text{x}+4\text{y}\div\text{y})}{(5\text{x}+6\text{y})\div\text{y}}$
$=\frac{3\big(\frac{\text{x}}{\text{y}}\big)+4}{5\big(\frac{\text{x}}{\text{y}}\big)+6}$
$=\frac{3(1)+4}{5(1)+6}\ [\text{From (1)}]$
$=\frac{3+4}{5+6}$
$=\frac{7}{11}$
Hence, the correct option is $(a)$.

Let the cost of one dozen bars be $Rs. x$
$\therefore$​ $30 : 5 = x : 12$
$\Rightarrow\text{x}=\frac{30}{5\times12}=\text{Rs. 72}$
Cost of one dozen $(12)$ bars $= Rs. 72$

$\big(\text{x}+\frac{1}{\text{x}}\big):\big(\text{x}-\frac{1}{\text{x}}\big)::5:4$
$\Rightarrow\frac{(\text{x}+\frac{1}{\text{x}})}{(\text{x}-\frac{1}{\text{x}})}=\frac{5}{4}$
$\Rightarrow\frac{\text{x}+\frac{1}{\text{x}}}{\text{x}+\frac{1}{\text{x}}}=\frac{5}{4}$
$5\text{x}^2-5=4\text{x}^2+4$
$\Rightarrow\text{x}^2=9\Rightarrow\text{x}=\pm3$

Total amount $= Rs\ 760$
Ratio $A : B = 8 : 11$
$\therefore\text{B}'\text{s}\text{ share}=\frac{760\times11}{8+11}$
$=\frac{760\times11}{19}$
$=\text{Rs. }440$

$\Rightarrow $ Ratio is a method of comparing two quantities by Division.
$\Rightarrow $ A common way to express a ratio is as a fraction in simplest form.
$\Rightarrow $ A ratio is a comparison of two similar quantities obtained by dividing one quantity by the other.

The total number of boys in school $= 1800$
The total number of student $= 3200$
Therefore the total number of girls $= 3200 - 1800 = 1400$
Therefore the ratio of $\frac{\text{girls}}{\text{boys}}=\frac{1400}{1800}$
ratio $= 7 : 9$