Directions: Study the following questions carefully and choose the right answer:
1
If a : b = 2 : 3 and b : c = 5 : 7, find the value of  a : b : c ?
» Explain it
C
Given  a  =  2  and  b  = 5 : 7
b 3 c

∴    a  =  ( a  ×  b )  =  ( 2  ×  5 )  =  10 .
c b c 3 7 21

So, a : c = 10 : 21.

Also, a : b = 2 : 3 and b : c = 5 : 7
 
 =  3  × 5 :  3  × 7 = 3 :  21
5 5 5

∴   a : b : c = 2 : 3 :  21  = 10 : 15 : 21.
5

Hence, option C is correct.

2
What is the fourth proportional to 3, 7, 15.
» Explain it
D
Let the fourth proportion be x. Then,

3 : 7 :: 15 : x.

∴   3x = 7 × 15

⇒  x =   ( 7 × 15 )  = 35.
3

Hence, option D is correct.

3
What is the mean proportion between 8 and 32.
» Explain it
C
Mean proportion =   8 × 32  =   256   = 16.

Hence, option C is correct.

4
What is the sub-duplicate ratio of 16 : 25.
» Explain it
B
Sub-duplicate ratio of 16 : 25 is  16  :  25   i.e. 4 : 5.

Hence, option B is correct.

5
Divide Rs.1024 in the ratio 9 : 7?
» Explain it
A
Sum of terms = (9 + 7) = 16.

First part = Rs. ( 1024 ×  9 )  = Rs. 576.
16

Second part = Rs. ( 1024 ×  7 )  = Rs. 448.
16

Hence, option A is correct.