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Answer:

Q20)A sum of ₹ 500 is in the form of notes of denominations of ₹ 5 and₹ 10. If the total number of notes is 90, find the number of notes of each type. The number of ₹ 10 notes = 90-x = 90-80 = 10 .

Step-by-step explanation:

Q20)A sum of ₹ 500 is in the form of notes of denominations of ₹ 5 and₹ 10. If the total number of notes is 90, find the number of notes of each type. The number of ₹ 10 notes = 90-x = 90-80 = 10 .

Given:

Total sum = 500

Total number of notes used = 90

To find:

Total number 5 and 10 rupees notes used

Solution:

Let,

total number of 5 rupee notes be [tex]x[/tex]

and total number of 10 rupee notes be [tex]y[/tex]

if we multiply the number of notes into the denominator we should get the total of 500. Hence,

[tex]5x + 10y= 500[/tex]

Let this be equation 1.

Since we know total number of notes are 90. Therefore,

[tex]x+y=90[/tex]

multiply both sides by 5 to have an equal value of [tex]x[/tex] as in equation 1. We get,

[tex]5x+5y=450[/tex]

Let this be equation 2.

Now, subtract equation 2 from equation 1 and solve for y.[tex]5x+10y-(5x+5y)=500-450\\5x+10y-5x-5y=50\\5y=50\\y=50/5\\y=10[/tex]

Insert the value of y in equation 1 and solve for x.

[tex]5x+10(10)= 500\\5x+100=500\\5x=500-100\\5x=400\\x=400/5\\x=80[/tex]

Therefore,

total number of 5 rupee notes = 80

and total number of 10 rupee notes = 10

Answer:

Solution:

L.C.M. of 4, 9 and 10 is 180.

Prime factors of 180 = 2 x 2 x 3 x 3 x 5

Here, prime factor 5 has no pair. Therefore 180 must be multiplied by 5 to make it a perfect square.

\therefore180\times5=900∴180×5=900

Hence, the smallest square number which is divisible by 4, 9 and 10 is 900.

Answer:

The smallest perfect square number which is exactly divisible by each of the 4, 6, 10 and 12 is 900 and [tex]\sqrt{900} [/tex] = 30

Step-by-step explanation:

We have to find the smallest perfect square number which is exactly divisible by each of the 4, 6, 10 and 12.

To find the smallest perfect square number which is exactly divisible by each of the 4, 6, 10 and 12, we have to first find the smallest number which is divisible by 4, 6, 10 and 12.

So, Smallest number divisible by 4, 6, 10 and 12 = LCM(4, 6, 10, 12).

[tex]\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:4 \: , \: 6\:, \: 10\:,\:12 \: \: }}}\\{\underline{\sf{2}}}&{\underline{\sf{\:\:2 \: , \: 3\:, \: 5\:,\:6 \: \: }}}\\ {\underline{\sf{3}}}&{\underline{\sf{\:\:1 \: , \: 3\:, \: 5\:,\:3 \: \: }}}\\{\underline{\sf{}}}&{\sf{\:1, \: \:1\:, \: 5 \:,\:1 \: }} \end{array}\end{gathered}\end{gathered}\end{gathered} \\ \\ \end{gathered} [/tex]

So,

[tex]\sf \:LCM(4, 6, 10, 12) = 2 \times 2 \times 3 \times 5 \\ \\ [/tex]

[tex]\sf\implies \sf \:LCM(4, 6, 10, 12) = 60 \\ \\ [/tex]

So, 60 is the smallest square number which is exactly divisible by each of the 4, 6, 10 and 12.

[tex]\sf \:Prime \: factorization \: of \: 60 = 2 \times 2 \times 3 \times 5 \\ \\[/tex]

We concluded from above factorization that prime factors 3 and 5 are not in pairs.

So, in order to get a perfect square, each factor of 60 must be in pairs.

[tex]\sf\implies 60 \: must \: be \: multiplied \: by \: 3\times 5 , \: i.e \: by \: 15 \\ \\[/tex]

[tex]\sf\implies Required\:number = 60 × 15 = 900 \\ \\[/tex]

Hence,

The smallest perfect square number which is exactly divisible by each of the 4, 6, 10 and 12 is 900

and

[tex]\sf \: \sqrt{900} = \sqrt{2.2.3.3.5.5} = 2.3.5 = 30 \\ \\ [/tex]

[tex]\rule{190pt}{2pt}[/tex]

Additional Information

[tex]\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{{More \: identities}}}} \\ \\ \bigstar \: \bf{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {x}^{2} - {y}^{2} = (x + y)(x - y)}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}\:\\ \\ \bigstar \: \bf{ {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) }\:\\ \\ \bigstar \: \bf{ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )}\: \end{array} }}\end{gathered}\end{gathered}\end{gathered}[/tex]

Answer:

The loss percentage is 10%

Step-by-step explanation:

Let the cost of 1 dozen oranges be x.

By selling oranges at the rate of 72 rs per dozen a woman loses 10% of her investment

1 dozen = 12 oranges

The cost of 12 oranges is Rs. 80.

The selling price of 100 oranges is 600. The selling price of 12 orange is

The selling price of 12 oranges is 72.

The formula for profit percentage is

Negative sign represent the loss.

Answer:

Anthrax causes a fatal blood disease known as sorter's disease.