Q1 of 7 Page 62

In which of the following sets are the numbers in proportion?

(1) 28, 16, 21, 12


(2) 12, 32, 15, 35


(3) 39, 26, 57, 38

Numbers a, b, c, d are said to be in proportion if



(1) Here,


a = 28, b = 16, c = 21, d = 12



On dividing numerator and denominator by 4 gives,



Now,



On dividing numerator and denominator by 3 gives,



From (i) and (ii)




∴ 28, 16, 21, 12 are in proportion


2) Here,


a = 12, b = 32, c = 15, d = 35



On dividing numerator and denominator by 4 gives,



Now,



On dividing numerator and denominator by 5 gives,



From (i) and (ii)



∴ 12, 32, 15, 35 are not in proportion


(3) Here,


a = 39, b = 26, c = 57, d = 38



On dividing numerator and denominator by 13 gives,



Now,



On dividing numerator and denominator by 19 gives,



From (i) and (ii)



∴ 39, 26, 57, 38 are in proportion


More from this chapter

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2

If the numbers in each of the following groups are in proportion, what is the value of the variable in each group?

(1) 6, x, 10, 15


(2) p, 9, 8, 6


(3) 25, 35, 35,m

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There is direct variation between the sale of books and the commission received for the sale. The table below gives the values of some sales and some commissions. Write the remaining values and complete the table.

 1

In each example, find the constant of proportionality and write the equation of variation.

(1) The quantity y varies directly as x. When the value of y is 20, the value of x is 4.


(2) p α q. When p is 12, the value of q is 18.


(3) c α d. When c = 28, d = 21.


(4) m α n. When m = 7.5, n = 10.

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Complete the following table showing an instance of inverse proportion. The table shows the number of workers carrying out a task and the number of days they take to do it.