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Q.

Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74. Find these numbers.


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a

2,3,4

b

4,5,6

c

7,8,9

d

10,11,12  

answer is C.

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Detailed Solution

It is given that three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74.
Let first integer be x, second integer as x+1 and,
Third integer as (x+1) +1=x+2x.
Multiplying the first integer by 2,
=2x
Multiplying the second integer by 3,
=3(x+1)
Multiply the third integer by 4,
=4(x+2)
It is given that sum of first, second and third number is 74.
⇒2x+3(x+1)+4(x+2)=74 ⇒2x+3x+4x+3+8=74 ⇒9x+11=74 ⇒9x=74−11  
Divide both the sides by 9.
9x=63 x=7  
Substitute the value of x in three integers,
First integer is,
x=7  
Second integer is,
=x+1 =7+1 =8  
Third integer is,
=x+2 =7+2 =9  
Hence, the three consecutive integers are 7,8 and 9.
Correct option is 3.
 
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Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74. Find these numbers.