Tag: equations from statements

Questions Related to equations from statements

Each child from a certain school can make $5$ items of handicraft in a day. If $1125$ handicraft items are to be displayed in an exhibition, then in how many days can $25$ children make these items?

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $6$ days

  2. $7$ days

  3. $8$ days

  4. $9$ days

Show answer
Correct Option: D
Explanation:

Number of handicrafts made by one student in a day = $5$


Total number of students = $25$

So, total number of handicrafts made in a day = $25\times5=125$

Total number of handicrafts required = $1125$

$\therefore$  Number of days required = $\dfrac{Total\ number\ of\ handicrafts\ required}{Number\ of\ handicrafts\ made\ in\ a\ day}=\dfrac{1125}{125}=9\ days$.

So, we can make the required number of handicrafts in $9\ days$.   $[D]$

Kiran spent $Rs. 6x$ on a book, $Rs. 6$ on food and had $Rs.18$ left. what was the sum of money she had at first? Express your answer in terms of $x$.

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $Rs. (6x+18)$

  2. $Rs. (6x+24)$

  3. $Rs. 64x$

  4. $Rs. 24x$

Show answer
Correct Option: B
Explanation:

Amount spent on book $=Rs. 6x$

Amount spent on food $=Rs. 6$
Total amount spent $=Rs. (6x+6)$
Amount left with Kiran $=Rs. 18$
$\therefore$ Amount she had at first $=Rs. (6x+6+18)$
                                            $=Rs. (6x+24)$

A person walks from his house at a speed of $4$ km/hr and reaches his schools $5$ minutes late. If his speed has been $5$ km/hr, he would have reached $10$ minutes earlier. The distance of the school from his house is

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $5$ km

  2. $6$ km

  3. $7$ km

  4. $8$ km

Show answer
Correct Option: A
Explanation:

Let the correct time to reach the school be ‘t’ hrs.

Then,the time taken by the man when he wakes at a speed of $4km$ will be ‘t’ hrs+5 mins,

which is nothing but $(t+\dfrac{5}{60})$hrs.

And,the time taken by the man when he walks at 5km/hr will similarly be $(t-\dfrac{10}{60})$hours.

As the distance in both the cases is same,

$4(t+\dfrac{5}{60}$)hrs=$5(t-\dfrac{10}{60})$hrs

$4t+\dfrac{20}{60}$=$5t-\dfrac{50}{60}$

 Therefore$ t=\dfrac{70}{60}$=$\dfrac{7}{6}$hrs

Actual distance=$4(t+\dfrac{5}{60})$

=  $4(\dfrac{70}{60}+\dfrac{5}{60})$

=$4\times \dfrac{75}{60}$=$5kms.$

If $12$ men complete a work in $20$ days. If only $8$ men are  employed, then the time required  to complete  the same work is

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $24$ days

  2. $25$ days

  3. $30$ days

  4. $35$ days

Show answer
Correct Option: C
Explanation:

As $12$ men complete work in $20$ days, $1$ man will complete the same work in

$20\times12=240$ days.

Time required by $8$ men to complete the work=$\dfrac{240}{8}$=$30$ days..

There are $50$ plates in a crate and there are $11$ such crates. When they are opened $\dfrac{2}{5}$ of the plates are found to be broken. How many plates are left intact?

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $220$

  2. $330$

  3. $530$

  4. $320$

Show answer
Correct Option: B
Explanation:
$\Rightarrow$Total number of crates$=11$

$\Rightarrow$one crates contain$= 50$plates

$\Rightarrow$so total number plates=$11\times50=550$

$\Rightarrow$the broken part of plates is $\dfrac{2}{5}$

$\Rightarrow$so the number of plates$=550\times\dfrac{2}{5}=220$

$\Rightarrow$the number plats left intact$=550-220=330$

Three friends, Mala, Leela and Sheela, divided a box of apples weighing $15\dfrac{9}{10}$ kg equally between the three of them. How many kgs of apples did each get?

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $5\dfrac{3}{10} kg$

  2. $3\dfrac{3}{10}  kg $

  3. $3\dfrac{9}{10}  kg $

  4. $5\dfrac{9}{10}  kg $

Show answer
Correct Option: A
Explanation:
Total weight of the apple $15\dfrac{9}{10}kg=\dfrac{(15\times10)+9}{10}=\dfrac{159}{10}$

There are three, they divide the apple equally between them

so one person will get the weight of apple $=\dfrac{159}{3\times10}=\dfrac{159}{30}=5\dfrac{3}{10}kg$