Tag: maths

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Questions Related to maths

Multiple choice maths be my multiple, i'll be your factor co-prime numbers lcm lowest common multiple (l.c.m.)

Select the correct option.
The HCF and the LCM of $12, 21, 15$ respectively are

  1. $3, 140$
  2. $12, 420$
  3. $3, 420$
  4. $420, 3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Numbers $= 12, 15, 21$


$12 =  2 \times 2 \times 3$


$15 = 3 \times 5$

$21 = 3 \times 7$

HCF = Product of smallest power of each common prime factor $= 3' = 3$
LCM = Product of greatest power of each prime factor 

$2^2 \times 3 \times 5 \times 7 = 4 \times 3 \times 5 \times 7 = 420$

$(C) \,\, 3, 420$

Multiple choice maths be my multiple, i'll be your factor co-prime numbers lcm lowest common multiple (l.c.m.)

The greatest number which when subtracted from 5834, gives a number exactly divisible by each of 20, 28, 32 and 35 is

  1. 1120

  2. 4714

  3. 5200

  4. 5600
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

 Number which is exactly divisible by 20, 28, 32 and 35 should be the common multiple of all these.
$20 = 2^2 \times 5$
$28 = 2^2 \times 7 \Rightarrow 32 = 2^5$
35.=5 $\times $ 7
LCM = $2^5 \times 5 \times 7 = 1120$
Hence the greatest number that should be subtracted
=5834-1120 = 4714

Multiple choice maths comparing quantities using proportion overhead expenses introduction to total cost price of the article profit and loss with overhead expenses

By selling 32 clips for a rupee, a man loses 40%. How many a rupee must he sell to gain 20%?

  1. 64

  2. 30

  3. 24

  4. 16
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

b'S.P. of 1 clip $\displaystyle=\frac{1}{32}$ of a rupee

$\implies$ 60% of CP $\displaystyle=\frac{1}{32}$ of a rupee

$\therefore$ 120% of CP $\displaystyle=\frac{1}{32}\times\frac{120}{60}$ i.e. $\displaystyle\frac{1}{16}$ of a rupee

$\implies$ he should sell 16 clips for a rupee.'

Multiple choice maths comparing quantities using proportion overhead expenses introduction to total cost price of the article profit and loss with overhead expenses

Reshma sells an article to Rekha at $37.5\%$ profit, Rekha sells it to Madhu at $9\dfrac{1}{11}\%$ profit. Again Madhu sells it to Mitu at $25\%$ loss. If Mitu pays $Rs\ 342$ for the article, then what is the cost price of the article to Reshma?

  1. $Rs\ 304$
  2. $Rs\ 266.50$
  3. $Rs\ 380$
  4. $Rs\ 384.75$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let CP be x. Reshma sells at 37.5% profit (1.375x). Rekha sells at 9 1/11% profit (1/11 fraction, so 12/11 * 1.375x). Madhu sells at 25% loss (0.75 * 12/11 * 1.375x = 342). Solving for x: 0.75 * 1.0909 * 1.375x = 342 -> 1.125x = 342 -> x = 304.

Multiple choice maths comparing quantities using proportion overhead expenses introduction to total cost price of the article profit and loss with overhead expenses

By selling a watch for Rs 480, a man gains 25%. How much per cent would he gain by selling it for Rs 432?

  1. $15\%$
  2. $\displaystyle6\frac{1}{4}\%$
  3. $\displaystyle12\frac{1}{2}\%$
  4. $25\%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Selling at 480 with 25% gain means CP = 480 / 1.25 = 384. Selling at 432 gives a gain of 432 - 384 = 48. Percentage gain = (48 / 384) * 100 = 12.5%.

Multiple choice maths comparing quantities using proportion overhead expenses introduction to total cost price of the article profit and loss with overhead expenses

Choose the correct answer from the alternatives given :
Mr. Ram runs a clothing store. His overhead expenses are 32% and his profits are 12% of his sale. At what price should he sell a raincoat which costs him Rs. 10.50 ?

  1. Rs. 13

  2. Rs. 15.52

  3. Rs. 12

  4. Rs. 19
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Cost price of umbrella $=Rs.10.50$
    overhead expenses $=32$% $=0.32$
            Required profit $=12$% $=0.12$
So, Selling price of umbrella $=Rs.10.50\times 1.32\times 1.12$
                                                $=Rs.15.52$
So, selling price $=Rs.10.50\times 1.32\times 1.12$
                           $=Rs.15.52$.
Multiple choice mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

What is the value of mean for the following data:

Marks No. of Student
$5-14$ $10$
$15-24$ $18$
$25-34$ $32$
$35-44$ $26$
$45-54$ $14$
$55-64$ $10$
  1. $30$
  2. $29$
  3. $33.68$
  4. $34.21$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To find the mean, use the formula (sum of f*x) / N. The midpoints (x) are 9.5, 19.5, 29.5, 39.5, 49.5, 59.5. Summing f*x gives 3368, and N is 100, resulting in 33.68.

Multiple choice mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

Mr. R purchases $20\ kgs$. of Wheat, $10\ kgs.$ of rice and $2\ kgs.$ of ghee every month. If the price of wheat is $Rs. 10$ per kg., price of rice is $Rs. 14$ per kg. and price of ghee is $Rs. 120$ per kg. Find the average price per kg. per month. Arithmetic mean $=$?

  1. $48$
  2. $18.125$
  3. $48.125$
  4. $18$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The average price per kg is the total cost divided by the total weight. Total cost = (20*10) + (10*14) + (2*120) = 200 + 140 + 240 = 580. Total weight = 20 + 10 + 2 = 32. Average = 580 / 32 = 18.125.

Multiple choice mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

If there are two groups containing $30$ and $20$ observations and having $50$ and $60$ as arithmetic means, then the combined arithmetic mean is ________.

  1. $55$
  2. $56$
  3. $54$
  4. $52$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Combined mean = (n1*x1 + n2*x2) / (n1 + n2). Calculation: (30*50 + 20*60) / (30 + 20) = (1500 + 1200) / 50 = 2700 / 50 = 54.

Multiple choice mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

What is the value of mean for the following data.

Class interval Frequency
$350-369$ $15$
$370-389$ $27$
$390-409$ $31$
$410-429$ $19$
$430-449$ $13$
$450-469$ $6$
  1. $400$
  2. $400.58$
  3. $394$
  4. $394.50$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Class Intervals Mid-values(x) Frequency(f) fx
$350-369$ $359.5$ $15$ $5,392.5$
$370.389$ $379.5$ $27$ $10,246.5$
$390-409$ $399.5$ $31$ $12,384.5$
$410-429$ $419.5$ $19$ $7,970.5$
$430-449$ $439.5$ $13$ $5,713.5$
$450-469$ $459.5$ $6$ $2,757$
$\displaystyle\sum f=111$ $\displaystyle\sum fx=44,464.5$

Arithmetic mean $=44,464.5/111=400.58$.