This is a direct application of the Family Budget Method — first find each item's own price relative $I$, then take the weighted average of these using $W$.

$I$: Food $=\dfrac{65}{50}(100)=130$; Clothing $=\dfrac{50}{40}(100)=125$; Fuel $=\dfrac{42}{30}(100)=140$; Housing $=\dfrac{130}{100}(100)=130$. …

The Family Budget Method first computes each item's own price relative, $I=\dfrac{p_1}{p_0}\times100$:

Next, multiply each item's price relative $I$ by its own budget weight $W$:

The weights already sum to $\Sigma W = 40+20+15+25=100$. Substituting into the Cost of Living Index formula:

$CLI=\dfrac{\Sigma IW}{\Sigma W}=\dfrac{13050}{100}=130.5$ …

Students sometimes average the price RELATIVES directly (a plain, unweighted average of the four $I$ values, which here would give $131.25$) instead of weighting each by $W$ first — since Food and Housing matter far more to this household's budget than Fuel or Clothin …