Question

The work done by a man, a woman and a child is in the ratio $3:2:1$. There are $20$ men, $30$ women and $36$ children. Their weekly wages (₹ $780$) are divided in the ratio of work done by men, women and children. What will be the wages of $15$ men, $21$ women and $30$ children for $2$ weeks? 

• A. ₹$585$
• B. ₹$292.5$
• C. ₹$1170$
• D. ₹$900$

Hint:

In mixed-work wage problems, first find each group's share via (count × rate) ratios, then convert to per-head and scale by time.

Answer 1

The Correct Option is C

Step 1: Let weekly per-head wage of man, woman, child be \(3k,2k,k\). Total weekly wage for \(20\) men, \(30\) women, \(36\) children: \[ 20(3k)+30(2k)+36(k)=156k=780 \Rightarrow k=5. \]

Step 2: Per-head weekly wage: man \(=₹15\), woman \(=₹10\), child \(=₹5\).

Step 3: For \(15\) men, \(21\) women, \(30\) children over \(2\) weeks: \[ 2(15\times15+21\times10+30\times5)=2(585)=\boxed{₹1170} \]