RD Sharma solution class 7 chapter 9 Ratio and Proportion Exercise 9.2

Exercise 9.2

Page-9.10

Question 1:

Which ratio is larger in the following pairs?
(i) 3 : 4 or 9 : 16
(ii) 15 : 16 or 24 : 25
(iii) 4 : 7 or 5 : 8
(iv) 9 : 20 or 8 : 13
(v) 1 : 2 or 13 : 27

Answer 1:

(i) Writing the ratios as fractions, we have
        3 : 4 = 34 and 9 : 16 = 916
     Now, LCM of 4 and 16 = 16.
     Making the denominator of each fraction = 16, we have
         34 = 3 × 44 × 4 = 1216 and the other fraction = 916
         Of 1216 and 916,  clearly 1216>916.
          Therefore, 34>916.
(ii) Writing the ratios as fractions, we have
        15 : 16 = 1516 and 24 : 25 = 2425
     Now, LCM of 16 and 25 = 400.
     Making the denominator of each fraction = 400, we have
         151615 × 2516 × 25= 375400 and the other fraction = 24 × 1625 × 16= 384400
        Clearly, 384 > 375. So, 384400 > 375400.
          Therefore, 2425>1516.
(iii) Writing the ratios as fractions, we have
        4 : 7 = 47 and 5 : 8 = 58
     Now, LCM of 7 and 8 = 56.
     Making the denominator of each fraction = 56, we have
            4× 87 × 8= 3256 and the other fraction = 5 × 78 × 7= 3556
        Clearly, 36 > 32. So, 3556 > 3256.
          Therefore, 58>47.
(iv) Writing the ratios as fractions, we have
       9 : 20 = 920 and 8 : 13 = 813
     Now, LCM of 20 and 13 = 260.
     Making the denominator of each fraction = 260, we have
          9× 1320 × 13= 117260 and the other fraction = 8 × 2013 × 20= 160260
        Clearly, 160 > 117. So, 160260 > 117260.
          Therefore, 813>920.
(v) Writing the ratios as fractions, we have
       1 : 2 = 12 and 13 : 27 = 1327
     Now, LCM of 2 and 27 = 54.
     Making the denominator of each fraction = 54, we have
          1× 272 × 27= 2754 and the other fraction = 13 × 227 × 2= 2654
        Clearly, 27 > 26. So, 2754 > 2654.
          Therefore, 12>1327.

Question 2:

Give two equivalent ratios of 6 : 8.

Answer 2:

We have
              68 = 6÷28÷2 = 34
     Therefore, 3 : 4 is an equivalent ratio of 6 : 8.
               68 = 6×28×2 = 1216
 Hence, 3 : 4 and 12 : 16 are equivalent ratios of 6 : 8.

Question 3:

Fill in the following blanks: 1220=   5=9   

Answer 3:

1220=  5= 9
 Let 1220= x 5= 9y.
Then, 1220= x 5 ⇒ 12 × 5 = 20x  ⇒ x = 12 × 520 = 3.
Also, 1220= 9 y ⇒ 12y = 20 × 9 ⇒ y = 20 × 912 = 15.
Therefore, 1220= 3 5= 915.

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