Question

set up all possible proportions from number 8,12,20 and 30​

Answer 1

Answer:

To solve this question, we will first break all the four numbers in multiples of primes, then using the definition of proportionality, we will solve each and every option and will see which option satisfies the condition of proportionality. After that, we will make a set of all possible proportions from the numbers given in the question.

Complete step by step answer:

Before we solve this question, let us see what makes two pairs of numbers in proportion.

Proportion says that two ratios or fractions are equal Suppose, we have two pairs of numbers, say a, b and c, d, then we can say that ( a, b ) and ( c, d ) are in proportion if ab=cd.

For example, 12=36, as on solving 36, we get 12.

Now, the number we have is 15, 18, 35, and 42.

So, firstly we factorize the number.

Then, 15=3×5 , 18=3×3×2, 35=7×5 and 42=7×3×2.

Now, 15 : 18 :: 35 : 42, means 1518::3542.

We can write 1518::3542 as 5×33×3×2::7×57×3×2

On solving, we get

53×2::53×2

56::56

Hence, option ( a ) is true.

Now, 15 : 35 :: 18 : 42, means 1535::1842.

We can write 1535::1842 as 5×37×5::3×3×27×3×2

On solving, we get

37::37

Hence, option ( b ) is true.

Now, 42 : 15 = 35 : 18, means 4215=3518.

We can write 4215=3518 as 7×3×25×3=7×53×3×2

On solving, we get

7×25=7×53×3×2

145≠3518

Hence, option ( c ) is not true.

Now, 42:35=18:15, means 4235=1815.

We can write 4235=1815 as 7×3×27×5=3×3×25×3

On solving, we get

3×25=3×25

65=65

Hence, option ( d ) is true.

So, set of possible proportion from the numbers 15, 18, 35 and 42 is = { 15:18 :: 35:42, 15:35 :: 18:42, 42:35 = 18:15 }

Note:

To solve such questions, one must know the meaning of proportionality, which means when two fractions are equal then we say fraction are in proportion. Also, we have to check each and every option so you must solve questions quickly but carefully too. Try not to make any calculation error.

Answer 2

Answer:

We note that 8 × 30 = 240 and 12 × 20 = 240

Thus, 8 × 30 = 12 × 20 ………..(I)

Hence, 8 : 12 = 20 : 30 ……….. (i)

We also note that, 8 × 30 = 20 × 12

Hence, 8 : 20 = 12 : 30 ……….. (ii)

(I) can also be written as 12 × 20 = 8 × 30

Hence, 12 : 8 = 30 : 20 ……….. (iii)

Last (I) can also be written as

12 : 30 = 8 : 20 ……….. (iv)

Thus, the required proportions are 8 : 12 = 20 : 30

8 : 20 = 12 : 30 12 : 8 = 30 : 20 12 : 30 = 8 : 20

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