Number 198 is divided into three parts such that 1/2 of the first part, 1/3 of the second part and 1/4 of the third part shall all be equal. Then the value of the largest part will be :

The correct answer is (C) 88.

Step-by-step mathematical working:

• Let the three parts of 198 be $x, y, z$.
• Given: $\frac{x}{2}=\frac{y}{3}=\frac{z}{4}=k$$\frac{x}{2}$ = $\frac{y}{3}$ = $\frac{z}{4}$ = k.
• Therefore: $x = 2k, \; y = 3k, \; z = 4k$.
• Sum of parts $= 2k + 3k + 4k = 9k = 198$$\implies$ k = $\frac{198}{9}$ = 22.
• The parts are: $x = 2(22) = 44, \; y = 3(22) = 66, \; z = 4(22) = 88$.
• The value of the largest part is 88.