Ages and Numbers

8/20/2019 Ages and Numbers

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Problems on Ages


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Content1) Introduction

2) Forming equations

3) Solving the questions by using general equation

4) Solving the questions by using tricks

5) Practice roblems

!) Problems on numbers

i"#ultile o$ the ratioii"%atio di$$erenceiii"&ivisible valuesiv"'hange in ratiov"&i$$erent timeline


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1) INTRODUCTION1) INTRODUCTION

It is easy to solve all these problems by equations but yourobjective in exam should be solving these problems in theeasiest way which saves more than half the time compared tosolving by equation.

The easiest way in solving these questions will be by pickingthe right answer among the four options using the ratio orthe values given in the question.


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2) Forming equations2) Forming equations

Statement Equation

A’s age 3 years later (after / hence / downthe line)

A+3

A’s age 3 years ago A-3

A is 3 years older than B A = B + 3

A is 3 years younger than B A = B - 3

A is 3 times (thrice) as old as B A = 3B

A is 3 times older than B (or)A is 3 times older to B

A = B + 3B =>A = 4B

ather was as old as his son at !resent" atthe time of his #irth$ - % = % => = &%

'he !resent age ratio of A and B is *$our years hence (or after) their age ratiowill #e *$

A/B = /*(A+4) / (B+4)= *$


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) !olving the questions "y using #$N$R%& $'U%TION) !olving the questions "y using #$N$R%& $'U%TION

$(ample The sum of the present ages of a son and hisfather is 6 years. !ix years ago" father#s age was five timesthe age of the son. $fter 6 years" what will be son#s age%

!&' ( 6')6 ( *+!)6,

!&6 ( %

-q becomes ')6 ( *! / 0 ' ( *! / 1

!ubstitute this is -q 23 ! & ' ( 6

! & +*! / 1, ( 6 6! ( 41

! ( 21 !&6 (

, The age of the son after 6 years is


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*) !olving the question "y using TRIC+!*) !olving the question "y using TRIC+!

$void using variables x 5 y always as there is a chance ofgoing wrong in relating the variables with the persons given.Instead" using the first letter will make the relating easy.'or example ! can be used as sons age and ' can be used asfathers age.


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Tri,- 1 .ultiple o/ the ratioTri,- 1 .ultiple o/ the ratio

$(ample 7resent ages of 8iran and !hyam are in the ratio

of * 3 1 respectively. Three years hence" the ratio of theirages will become 22 3 9 respectively. :hat is !hyam#spresent age in years%

$.1

;.C.6


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(o* The age of +iran an0 !hyam is in the ratio *., !hyams age should be in the multiple o/ *.

=nly option a and d are having the age of !hyam in themultiple of 1. The answer should be either a)2* or 0)23

+$ter 3 years*

8irans age / a)2*4526 or 0)2451 The age of +iran an0 !hyam will be in the ratio 117. , !hyams age should be in the multiple o/ 7.

=nly a)26 is in the multiple o/ 7., !hyams present age is a)2*.


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Example 1. ne year ago" the ratio of %oora.s and0imals age was * res!ecti1ely$ our years hence"this ratio would #ecome 2$ ow old is 0imal

A$445earsB$43 years

6$47 5ears8$3* 5ears


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Tri,- 2 Ratio 0i//eren,eTri,- 2 Ratio 0i//eren,e

$(ample $lan is younger than Turing by 6 years and their

ages are in the respective ratio of > 3 9" how old is Turing%

$.24;.>C.0*


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The age of $lan and Turing is in the ratio 67.The age 0i//eren,e between them is 8.

-quate the ratio difference and age difference

67

2 parts

6

parts ( 6

2 part ( 09 parts ( >

, The age of Turing is >


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Example 2. 'he ratio #etween the !resent ages of 9and : is *$ ;f : is 4 years old than 9" what will #ethe ratio of the ages of 9 and : after 4 years$

A)7

B)326)2

8)2


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Tri,- Divisi"le valuesTri,- Divisi"le values

$(ample $ person#s present age is two)fifth of the age of

his mother. $fter 4 years" he will be one)half of the age of hismother. :hat is the present age of the mother%

$.6;.1*

C.1


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(o* 95 2: . This indicates that . should be 0ivisi"le "y . =nly options b, * and c, *; are divisible by *.

+$ter , years*

?&4( ") *4 5 or ,)*;4 5 *

94 5


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Example 3. %andee!s age after si< years will #ethree-se1enth of his fathers age$ 'en years ago theratio of their ages was $ hat is %andee!sfathers age at !resent

A$ 43 5ears

B$ *?5ears6$ ? 5ears8$ * 5ears


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Tri,- * Change in ratioTri,- * Change in ratio

$(ample 'ather is aged three times of his son !unil. $fter 4

years" he would be two and a half times of !unil#s age. $fterfurther 4 years" how many times would he be of !unil#s age%

$. times;.0 times

C.1 times


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(o * F! 5 1 +$ter , years * F! 5 2 @ 32

=nly option a) 2 is less than @


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Example 4. 'he age of father ? years ago wasthrice the age of his son$ 'en years hence"fathers age will #e twice that of his son$ hat isthe ratio of their !resent ages

A$*7

B$36$348$


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Tri,- Di//erent timelineTri,- Di//erent timeline

$(ample $yesha#s father was 04 years of age when she

was born while her mother was 06 years old when herbrother four years younger to her was born. :hat is thedifference between the ages of her parents%

$.6 Aears

;.* AearsC.> Aears


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$yesha#s 'ather was years ol0 when she was "orn F % ;Ber ?other was 8 years ol0 when her ;rother was "orn. . ?8;Ber ;rother is /our years younger to her? %; *

$s these three equations are not in the same timeline" compare thevalues and make it same.

$q 2 @ $q The common value ? is already same.$q 1 @ $q $( 5 $(1. To make it equal a00 * with eq2.

F %*2* , F % . ?

*2 * 8 ;The 0i//eren,e "etween F an0 . is 83


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Example 5. A father said to his son" @; was as oldas you are at the !resent at the time of your #irth@$;f the fathers age is 32 years now" what was thesons age 1e years #ac

A$4 5ears

B$ 5ears6$* 5ears8$2 5ears


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) 9ra,ti,e pro"lems) 9ra,ti,e pro"lems


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:$ 'he total age of A and B is & years more thanthe total age of B and 6$ 6 is how many yearyounger than A

A$&B$3

6$48$


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:&$'he sum of ages of children #orn at the

inter1als of 3 years each is ? years$ hat is theage of the youngest child

A$&B$4

6$*8$?


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:3$Ages of two !erson diCer #y * years$ ;f * yearago" the elder one #e 3 times as old the youngerone" nd their !resent age$

A$3*" *B$3?" 4

6$&4" 28$3?" ?


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:4$ %te1e is older than Dar #y * years$ ;f the ratioof their current ages is 7" what will #e thecorres!onding new ratio of their ages when Dar istwice as old as he is now

A$2

B$46$378$4


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9ro#lems n Fum#ers


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!ome ?asi, Formulae!ome ?asi, Formulae

+a & b,+a ) b, ( +a ) b,+a & b, ( +a & b & ab,+a ) b, ( +a & b ) ab,+a & b & c , ( a & b & c & +ab & bc & ca,+a0 & b0, ( +a & b,+a ) ab & b,

+a0 ) b0, ( +a ) b,+a & ab & b,+a0 & b0 & c 0 ) 0abc , ( +a & b & c ,+a & b & c ) ab ) bc ) ac ,:hen a & b & c ( " then a0 & b0 & c 0 ( 0abc .


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$ two 0igit num"er can be represented as 1;(4y where xand y are the two digits.

!imilarly a three 0igit num"er as 1;;(41;y4A and so on.


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Q1. If one-third of one-fourth of a number is 15, then

three-tenth of that number is:

A.54

B.45

C.36D.58


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Q. !he differen"e bet#een a t#o-di$it number and the

number obtained b% inter"han$in$ the di$its is 36.&hat is the differen"e bet#een the sum and the

differen"e of the di$its of the number if the ratio

bet#een the di$its of the number is 1 : '

A.8

B.16

C.4

D.1


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Q3. !hree times the first of three "onse"uti(e odd

inte$ers is 3 more than t#i"e the third. !he third inte$eris:

A.15

B.14C.1

D.1)


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Q4. A t#o-di$it number is su"h that the *rodu"t of the

di$its is 8. &hen 18 is added to the number, then thedi$its are re(ersed. !he number is:

A.4

B.1C.48

D.6


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Q5. In a t#o-di$it, if it is +no#n that its units di$it

e"eeds its tens di$it b% and that the *rodu"t of the$i(en number and the sum of its di$its is eua/ to 144,

then the number is:

A.4B.6

C.8

D.30

.3


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Ages and Numbers

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