Viral Maths Problem Confusing Students & Parents

There are 73 red, blue and green marbles in a jar. There are twice as many red marbles as blue marbles. There are 19 more marbles than green marbles. 

How many green marbles are there?

Check if you are correct! 

Solution of Viral Maths Problem Confusing Students & Parents

What was the problem?

Using Algebra : 

Let r,b and g be the numbers of red, blue and green marbles in the jar.

There are 73 red, blue and green marbles in a jar.

So r + b + g = 73    .....(1)

There are twice as many red marbles as blue marbles.

r = 2b                  ......(2)

There are 19 more blue marbles than green marbles. 

b = g + 19            

g = b - 19            ......(3)

Putting (2) and (3) in (1), gives

2b + b + b - 19 = 73

4b = 92

b = 23

Putting b = 23 in (3) gives,

g = 23 - 19 = 4

Putting  b = 23 in (2), gives 

r = 2x23 = 46

So there are 46 red,23 blue and 4 green marbles in the jar.

Without Algebra :

In the case, we need to try trail and error method.

If g = 1, then b = 20 and r = 2(20) = 40 giving total 40 + 20 + 1 = 61.

If g = 2, then b = 21 and r = 2(21) = 42 giving total 42 + 21 + 2 = 65.

If g = 3, then b = 22 and r = 2(22) = 44 giving total 44 + 22 + 3 = 69.

Total is increasing at the rate of 4. So finally,

If g = 4, then b = 23 and r = 2(23) = 46 giving total 46 + 23 + 4 = 73.


So there are 46 red,23 blue and 4 green marbles in the jar.

The Buyer Who is Thief

Once a man steals Rs.100 note from the shop. Later he purchases good of worth Rs.70 from the same shop using that note. The shopkeeper gives back Rs.30 in return. 

How much did shopkeeper loose in the case?


Do you think Rs.130? Or anything else? 

Loss Due To Thief Buyer

What's the case history? 

So did you just answer Rs.130 ? No, that's not correct!

Thief initially steals Rs.100 note. Now imagine instead of Rs.100 he steals goods of worth Rs. 70 + Rs.30 (given by shopkeeper). So eventually, the shopkeeper lost only Rs.100 in the process. 

In other words, the thief exchanges Rs.70 with the goods in the case. He pays for those goods to shopkeeper. So he looses Rs.70 from stolen Rs.100 & gains back via goods.

So eventually, the shopkeeper lost only Rs.100 in the case.

 

The Exact Age?

Tommy: "How old are you, Mamma?"

Mamma: "Let me think, Tommy. Well, our three ages add up to exactly seventy years."

Tommy: "That's a lot, isn't it? And how old are you, Papa?"

Papa: "Just six times as old as you, my son."

Tommy: "Shall I ever be half as old as you, Papa?"

Papa: "Yes, Tommy; and when that happens our three ages will add up to exactly twice as much as to-day."

Tommy: "And supposing I was born before you, Papa; and supposing Mamma had forgot all about it, and hadn't been at home when I came; and supposing..."

Mamma: "Supposing, Tommy, we talk about bed. Come along, darling. You'll have a headache."

Now, if Tommy had been some years older he might have calculated the exact ages of his parents from the information they had given him. Can you find out the exact age of Mamma?

Here is CALCULATION of exact age!

Calculation Of The Exact Age

What was the problem? 

Let us suppose T be the age of Tommy, M be of the Mamma and P be that of Papa.

Sum of their ages is 70.

T + M + P = 70  ......(1)

and Papa is 6 times as old as Tommy,

P = 6T  .....(2)

In unknown number of years X, Papa will be twice old as Tommy,

P + X = 2 (T + X)  ....(3)

and the sum of ages at that time is 70 x 2 = 140,

(T + X) + (P + X) + (M + X) = 140.

T + P + M + 3X = 140

From (1), above equation becomes,

70 + 3X = 140

X = 70/3     .....(4)

Putting (4) and (2) in (3),

P + X = 2 (T + X) 

6T + 70/3 = 2(T + 70/3)

T = 70/12    .....(6)

Using (6) in (2),

P = 6T

P = 6(70/12)

P = 70/2    ......(7)

Putting (6) and (7) in (1),

M = 70 - 70/2 - 70/12

M = 29.1666 = 29 years 2 months.

P = 70/2 = 35 years.

T = 70/12 = 5.8333 = 5 years 10 months.

 
To summarize, the Tommy is 5 years 10 months old, Mama is 29 years 2 months old and Papa is 35 years old.

50th Fastest And The 50th Slowest

Matt is the fiftieth fastest and the fiftieth slowest runner in his school.

Assuming no two runners are the same speed, how many runners are in Matt’s school?

Find here total number of runners!