Let’s solve these arithmetic questions

Hyderabad: If a : (b c) = b : (c a) = c : (a b) and a b c =/ (not equal) 0, then the value of b : (a b c) is?

a) 1 : 1 b) 1 : 2 c) 1 : 3 d) 1 : 4
Ans: c
Solution: a/ b c = b/ c a
By componendo and dividend
a b c/ a – b – c = b c a/ b – c – a
a – b – c = b – c – a
a = b
Similarly, b = c and c = a
Therefore, a = b = c
b : (a b c) = 1 : 3
If 2r = h r2 h2, (r =/0), then find r : h.

a) 1 : 2 b) 2 : 1 c) 3 : 4 d) 4 : 3

Ans: d

Solution: 2r – h = r2 h2

(2r – h)² = (r2 h2)2

4r² h² – 4rh = ( r2 h2)2

3r² = 4rh

r/h = 4/3
r : h = 4 : 3
If the ratio of boys to girls in a class is B and the ratio of girls to boys is G, the value of 3(B G) is equal to?

a) Equal to 3 b) Greater than 3 c) Less than 3 d) Equal to 1

Ans: b

Solution: Boys : Girls = B : 1
Girls : Boys = G : 1
Clearly, B = 1/G
B G = 1/G G >; 1

( The sum of any positive fraction and its inverse is always greater than 1)

3 (B G ) >; 3

If a/ b c – a = b/ a c – b = c/ a b – c = k, then value of k is?

a) a/b b) b/c c) c/a d) None of the above

Ans: d

Solution: a b c/ (b c – a) (a c – b) (a b – c) = k

a b c/ a b c = 1
k = 1