Question

The expenses of rice, fish and oil of a family are in the ratio $12:17:3$. The price of these articles are increased by $20$%, $30$% and $50$% respectively. The total expenses of family on these articles are increased by:

Answer 1

Rice =$12x$

Fish =$17x$

Oil =$3x$

Total $=32x$

Now , rice $=12x+\frac{20}{100}12x$

$=\frac{120}{100}\left(12x\right)$

Fish $=17x+\frac{30}{100}17x=\frac{130}{100}\left(17x\right)$

oil $=3x+\frac{50}{100}3x=\frac{150}{100}\left(3x\right)$

Total now=$\frac{120\left(12x\right)+130\left(17x\right)+\left(150\right)\left(3x\right)}{100}$

$=\frac{4100x}{100}=41x$

$\%$ increased $\to y$

$32x+\frac{y}{100}32x=41x$

$32x\left(\frac{100+y}{100}\right)=41x$

$100+y=\frac{4100}{32}=128.125$

$y=128.125\%$