Problems on Ages with Shortcuts

1. The average age of Ram, Venu, Kumar, Gopal and Ragav is 28 years. The average age of Gopal and Ragav is 25 years. What is the average age of Ram, Venu and Kumar ?

Solution :

Here 5 persons' average ( Ram, Venu, Kumar, Gopal and Ragav) age is  = 28 Years.

That means their total age = 5 X 28 = 140 Years.

similarly, average age of two persons (Gopal and Ragav)  is 25 years.

So their total age = 25 X 2 = 50 Years.

here 140 years is the total age of 5 persons             ( Ram, Venu, Kumar, Gopal and Ragav)

50 years is the total age of 2 persons (Gopal and Ragav)

So obviously, the total age of Ram, Venu and Kumar = Total age of  ( Ram, Venu, Kumar, Gopal and Ragav) - Total age of (Gopal and Ragav)

= 140-50 = 90 years.

But here we need average age of these 3 persons.

=> 90/3  = 30 Years

Shortcut Method :

((5 X 28) - (2 X 25)) / 3 =  (140-50)/ 3 = 90/3 = 30 Years

2. The ratio between the ages of Keerthi and Sony is 5:8 respectively and difference between their ages after 5 years will be 12 years. What is the present age of Keerthi ?

Solution :

Usually for these type of questions people start with present age as X and adding 5 to get the ages after 5 years and later solve those equations. But its very time consuming.

A simple logic here is if the age difference between you and your friend is 8 years, after 5 or 10 years also the difference will be same. Hope you are getting what I am trying to say ;)

now see, the ratio between their ages is 5 : 8 

That means their actual ages will be some 5X and 8X

Then the difference between their ages is 5X-8X

in the question it is given that the difference is 12 years =>  5X-8X = 12  => 3X=12  => X = 4

So obviously Keerthi's age = 5(4) = 20

3. Sony is 30 years younger than his mother Rani. Five years ago, Sony was 1/4 as old as his mother was. How old is Sony today ?

Solution :

5 years ago the ratio between their ages was Sony : Jay a= 1X : 4X

we know that Hari is 30 years younger than Rani. That means the difference between their ages is 30.

=>   3X = 30  => X = 10.

But this is the age of 5 years ago. So, the present age will be =10+5 = 15 Years

4. At present the ratio of the ages of Anand and Venkat is 4 : 7 respectively. 6 years hence it will be 7 : 10 respectively. What is the present age of Venkat ?

Solution :

Present ratio of their ages is 4 : 7 (So their present ages will be 4X, 7X)

After six years it will be of 7 : 10

=> (4x+6) : (7x+6) = 7 : 10

=> 40x + 60 = 49X + 42 (Cross Multiplication)

=> 9x = 18

=> x = 2                          

So Venkat's present age will be 7X2 = 14 Years

Shortcut :

There is a shortcut formula for finding X

here, New ratio difference is 3, Added number is 6 (years)

Cross multiplication difference is 49-40 = 9

=>       X = (3 x 6) / 9  = 2

So Venkat's present age will be 7X2 = 14 Years

5. Ten years ago the ratio between the ages of Mohan and Suman was 3:5 respectively. 11 years hence it will be 11:16 respectively. What is the present age of Mohan?

Solution :

 10 years ago 3x : 5x  -------------> Old Ratio

11 years hence  11x : 16x       ------------->  New Ratio

here the difference between ages is 21 years (10 years ago + 11 years hence)

apply above formula here

New ratio difference is (16-11) = 5

Added or substracted number (difference between ages) is = 21

Old and new ratios cross multiplication difference is = 55 - 48 = 7

==> X = (5 x 21) / 7 = 15

present age of mohan is = his age of 10 years ago + 10

                               

                                            = 3x15 + 10 = 55 years

6. Amar is as much younger than Raja as he is older than Kiran. If the ages of Amar and Raja are 30 years and 36 years respectively, what is the age of Kiran now ?

Solution :

Simple logic....

Amar is as much younger than Raja as he is older than Kiran. Try to understand this sentence. According to this sentence you can understand that

·         Amar is younger than Raja that means there is some X years difference between Amar and Raja.

·         Amar is older than Kiranwith same age difference (X years) between Amar and Kiran.

But we know that the ages of Amar and Raja are 30 and 36 years.

So the difference between their ages is = 6 years

So the difference between Amar and Kiran should be = 6 years.

We know the age of Amar as 30 years and Kiran is younger than Amar for 6 years. So he should be of 24 years.

With a single glance you can calculate answer for these type of problems.

7. The average age of a class of 20 students is 20 years. When the age of the teacher is also included, the average will be increased by 2 years. What is the age of the teacher ?

Solution :

Simple logic,

we know that 20 students' average = 20 years

20 people total age = 20 x 20 = 400 years

Including Teacher's

21 people average = 22 years

21 people total age = 21 x 22 = 462

we know the age of 20 students = 400 Yeras

we know the age of 21 people (20 students+ Teacher) = 462

so the age of Teacher will be 462-400 = 62 Years

8. The average age of a wife and husband, who were married 10 years ago, was 20 years then. Including a child the present average age of the family is 23 years. What is the present age of the child?

Solution :

10 year's ago average age = 20 years

10 year's ago total age = 20 x 2 = 40 years.

to calculate their present total age, you should add 20 (10 for wife and 10 for husband) to the age of 10 years ago

=> 40+20 = 60 years (this is the present age of husband and wife)    ----------- (1)

according to the given data, present average age of the family of 3 members is = 23 years

so Total age of 3 members = 23 x 3 = 69 years. ------------------(2)

but we know the present age of Husband and Wife = 60 years

so from equations (1) and (2), we can get the present age of the child is = 9 years

9. Five years ago the average age of a family of five members was 27 years then. Including a child the present average age is still same today. What is the age of the child now ?

Solution :

5 years back average = 27 years

present average should be 5 +27 = 32 Years

So total age of the 5 members at present = 5 x 32 = 160 years  -----------------(1)

but its given that including the child, the present average is 27 years.

=>   the total age of 6 members at present = 6 x 27 = 162 years -----------------(2) 

so from (1) and (2), you can easily get that the present age of the child is 2 years

10. The ratio between the ages of Karan and Arjun is 9:5 and sum of their ages at present is 56 years. How old will karan be after 4 years ?

Solution :

according to given data their ages should be 9x, 5x

their present age = 9x+5x = 56  ==> 14x = 56

so x = 4

so present age of Karan is 9 x 4 = 36 years

after 4 years, 36+4 = 40 years :)

Twinkies and Root Beer

A little boy wanted to meet God. He knew it was a long trip to where God lived, so he packed his suitcase with Twinkies and a six-pack of Root Beer and he started his journey.

When he had gone about three blocks, he met an elderly man. The man was sitting in the park just feeding some pigeons.

The boy sat down next to him and opened his suitcase. He was about to take a drink from his root beer when he noticed that the man looked hungry, so he offered him a Twinkie.

The man gratefully accepted it and smiled at boy. His smile was so pleasant that the boy wanted to see it again, so he offered him a root beer.

Again, the man smiled at him. The boy was delighted! They sat there all afternoon eating and smiling, but they never said a word.

As it grew dark, the boy realized how tired he was and he got up to leave, but before he had gone more than a few steps, he turned around, ran back to the man, and gave him a hug. The man gave him his biggest smile ever.

When the boy opened the door to his own house a short time later, his mother was surprised by the look of joy on his face. She asked him, "What did you do today that made you so happy?
"He replied, "I had lunch with God." But before his mother could respond, he added, "You know what? God's got the most beautiful smile I've ever seen!"

Meanwhile, the elderly man, also radiant with joy, returned to his home. His son was stunned by the look of peace on his face and he asked," Dad, what did you do today that made you so happy?"
He replied, "I ate Twinkies in the park with God." However, before his son responded, he added," You know, he's much younger than I expected."


People come into our lives for a reason, a season, or a lifetime.
Embrace all equally!

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Spilled Apples

A few years ago a group of salesmen went to a regional sales convention in Chicago. They had assured their families that they would be home in plenty of time for Friday night's dinner.

In their rush, with tickets and briefcases, one of these salesmen inadvertently kicked over a table which held a display of baskets of apples. Apples flew everywhere. Without stopping or looking back, they all managed to reach the plane in time for their nearly missed boarding. All but one. He paused, took a deep breath, got in touch with his feelings, and experienced a twinge of compassion for the girl whose apple stand had been overturned.

He told his buddies to go on without him, waved goodbye, told one of them to call his wife when they arrived at their home destination and explain his taking a later flight. Then he returned to the terminal where the apples were all over the terminal floor.  He was glad he did.

The 16 year old girl was totally blind! She was softly crying, tears running down her cheeks in frustration, and at the same time helplessly groping for her spilled produce as the crowd swirled about her, no one stopping, and no one to care for her plight. The salesman knelt on the floor with her, gathered up the apples, put them into the baskets, and helped set the display up once more. As he did this, he

noticed that many of them had become battered and bruised; these he set aside in another basket. When he had finished, he pulled out his wallet and said to the girl, "Here, please take this $20 for the damage we did. Are you okay?"

She nodded through her tears. He continued on with, "I hope we didn't spoil your day too badly."
As the salesman started to walk away, the bewildered blind girl called out to him, "Mister..." He paused and turned to look back into those blind eyes.  She continued, "Are you Jesus?"

He stopped in mid-stride, and he wondered. Then slowly he made his way to catch the later flight with that question burning and bouncing about in his soul: "Are you Jesus?"
Do people mistake you for Jesus?

That's our destiny, is it not? To be so much like Jesus that people cannot tell the difference as we live and interact with a world that is blind to His love, life and grace.

If we claim to know Him, we should live, walk and act as He would.  Knowing Him is more than simply quoting Scripture and going to church.  It's actually living the Word as life unfolds day to day. You are the apple of His eye even though we, too, have been bruised by a fall. He stopped what He was doing and picked you and me up on a hill called Calvary and paid in full for our damaged fruit.
Let us live like we are worth the price He paid.  Think about it.

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