Question

The sum of three numbers is 98. The ratio of the first to the second is 2/3, and the ratio of the second to the third is 5/8. The second number is:

(a) 15, (b) 20, (c) 30, (d) 32, (e) 33

Answer 1

Let The Numbers Be x , y and z
Then,

x + y + z = 98 ----[Given]

x : y = 2 / 3
x = 2y / 3

y : z = 5 / 8
Using Invertendo --[It means Making Numerator Denominator and
z : y = 8 / 5                 making Denominator Numerator Its There in
z = 8y / 5                     10th std ICSE syllabus] 

Now,
x + y + z = 98

Substituting The Value of x and z in the given equation
 
2y  +  y  + 8y  =  98
----            ----                                   
 3               5
 LCM = 15
 
 10y + 15y + 24y  =  98
 ----------------------    
            15
            
49y = 98 * 15
y = 98 * 15 
      ---------- 
           49
y = 2 * 15
y = 30

So,
The Second Number = 30

ANSWER = (C) = 30

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Answer 2

Let the three numbers be x, y and z.

Now,
Its given that their sum is 98.

So, x + y + z = 98 --Eq.1

Again, given ratios –
x : y = 2 : 3 --Eq.2
y : z = 5 : 8 --Eq.3

So, now we have to find the second number i.e. y


Finding the value of x in terms of y.
Using Eq.2, we can write
x/y = 2/3
x = 2y/3 --Eq.4

Now, again finding the value of z in terms of y.
Using Eq.3, we can write
y/z = 5/8
z = 8y/5 --Eq.5

Putting the values of x and z according to Eq.4 and Eq.5 in Eq.1

x + y + z = 98
2y/3 + y + 8y/5 = 98

Making the denominators common

10y/15 + 15y/15 + 24y/15 = 98
49y/15 = 98

Transposing 15 and 49 to RHS

y = 98×15/49
y = 2 × 15
y = 30

So, the answer is (C)30