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Jun

Examples

(1) In what proportion must rice at Rs. 12.50 per kg. be mixed with rice at Rs. 15.20 per kg., so that the mixture be worth Rs. 14.00 per kg. ?

Solution.

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Jun

ALLIGATION OR MIXTURE

☼ Alligations is the rule that helps us to find the amount in which two different quantities of a substance are mixed so as to arrive at average cost.

☼ If the gradients are mixed in some ratio, then

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Jun

Examples(2)

(8) If a, b, c, d are four consecutive odd integers, then give its average in the form of a.

Soln. A b c

Here, a, b, c, d are in A.P.

$\th... </p> <div class=$

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Jun

Examples

Examples :

(1) Find the average of first 7 prime numbers.

Soln. Required average = $\left (\frac{2+3+5+7+11+13+17}{7} \right )$

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Jun

Harmonic Mean

☼ Harmonic Mean : If the reciprocals of the terms is an arithmetic series is taken and then summed up, then the number of observations divided by the sum is defined as Harmonic mean.

Harmonic mean of

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Jun

Geometric Mean

☼ Geometric Mean : The geometric mean (G.M.) of n numbers is the nth root of the product of the n numbers.

Therefore, Geometric mean of $a_{... </p> <div class=$

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Jun

Arithmetic Mean

☼ Arithmetic Mean : The arithmetic mean of n numbers $x_{1}, x_{2},x_{3},...,x_{n}$ is denoted by and is calc…

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Jun

Average

☼ Average : An average is a single value that is in some way indicative of a group of values. The most commonly used average is arithmetic mean (AM) or simply the average ( $\overline... </p> <div class=$

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Jun

Example(3)

(21) Find the lowest number which when subtracted from 10000, is exactly divisible by 15, 27 and 24.

Soln. L.C.M. of 15, 27 and 24 = 1080.

If we divide 10000 by 1080, we get the remainder = 280

i.e. If 280 i…

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Jun

Examples(2)

(11) Greatest number which can divide 327, 352, 200 leaving respectively 12, 7, 5 as remainders, is :

Soln. Required number = H.C.F. of ( 327 – 12 ), ( 352 – 7 ), ( 200 – 5 )

= H.C.F. of 315, 345, 195
…

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