EXERCISE 7A (OBJECTIVE TYPE QUESTIONS IN 31 35 SOLUTION )

31.       One-fifth of a number is equal to 5/8 of another number. If 35is added to the first number, it becomes four times of the second number. The second number is:

a)      25

b)      40

c)       70

d)      125

32.       The sum of two numbers is 25 and their difference is 13. Find their product.

a)      104

b)      114

c)       315

d)      325

33.        If the sum of two numbers is 33 and their difference is 15, the smaller numbers is:

a)      9

b)      12

c)       15

d)      18

34.       The sum, of two numbers is 40 and their difference is 4. The ratio of the numbers is:

a)      11: 9

b)      11:18

c)       21:19

d)      22:9

35.       The product of two numbers is 192 and the sum of these two numbers is 28, what is the smaller of these two numbers?

a)      12

b)      14

c)       16

d)      18

e)      None of these 

ANSWERS 

31.B

32.B

33.A

34.A

35.A

SOLUTION 

31.       Let the numbers be X and y. then, 1/5 X = 5/ 8 y   Y = 8 /25x.

Now, X + 35 = 4y X + 35 = 32 / 25x    7/ 25X = 35    X = ( 35 x 25 / 7 ) = 125.

Second number = y = 8 / 25 x = ( 8 / 25 x 125 ) = 40.

32.       Lt the numbers be x and Y. Then,  + y = 25 and X – Y = 13.

4X Y = ( x + y )² - (x – y_² = (25)² - (13)² = 625 – 169 = 456  XY = 114.

33.       Let the numbers be x an Y

Then, x + y = 33

                 

Solving (I) and (II), we get: x = 24, Y = 9.

Smaller number = 9.

34.       Let the numbers be X an y. then,

X + y / X – Y = 40 / 4 = 10  ( X + y) = 10 (  -Y)    9x = 11y    x / Y = 11/ 9.

35.       Let the numbers be x and (28 – x). then,

X(28 – X) = 192  x² - 28X + 192 = 0  (X – 16) (x -12) = 0

X = 16 or   12.

So, the numbers are 16 and 12.