A says to B I am twice as old as you were when I was as old as you are. The sum of their ages is 49 yrs. Find?

Question

their ages.
2)A train travels from Y to Z at 60km/hr and from Z to Y at 40km/hr. Find the average speed.
3)1729 can be expressed as the cube of two numbers. One is ten cube + 9 cube. What are the other two cubes. What's interesting about this expression. ( Episode related to Srinivasan and Prof Hardy)
4) What is anomolous expansion of water?

Answer 1

1)
A+B=49 therefore B=49-A

A=2(B-(A-B); thus
A=2((49-A)-(A-(49-A)))
A=2((49-A)-(A-49+A)))
A=2(49-A-A+49-A)
A=2(98-3A)
A=196-6A
7A=196
A=28;B=49-28=21

When A was 21, B was 14; 28 is twice 14.

2)
Suppose dist YZ = 120km
@60km/hr, time = 2h; at 40km, time = 3h.
240km/5h = 48km/h

3)
12^3 + 1^3

4)
Nearly all materials expand when heated, and contract when cooled. Water expands when heated, and expands when cooled. This keeps our oceans from freezing, as the pressure against such enormous expansion keeps it from happening.

Answer 2

Let me just answer part 3.
The other 2 cubes are 12³ and 1³.
1729 is the smallest positive integer expressible
as the sum of 2 cubes in 2 different ways.
BTW 1729 is also the 3rd largest Carmichael number.
Look up Carmichael numbers in Wikipedia for
an interesting explanation!

Answer 3

A + B = 49 ----(1)
A = 2(B-n) ----(2)where n is the number of years that past
A - n =B ------(3)

n=A - B replace n in (2)
A = 2(B - A + B)
A = 4B - 2A
3A =4B => A = 4/3 B
replace A in (1)
4/3 B + B = 49 => 7/3 B = 49 => B = 21 and A = 28

2) (60 + 40)/2 = 50 km/hr

3) and 4) I dunno

Answer 4

I personally think your questions have been worded wrong, Not enough information is given.

Answer 5

the answer is always c