A manufacturer undertakes to supply $2000$ pieces of a particular component at $Rs.\, 25$ per piece. According to his estimates, even if $5 \%$ fail to pass the quality tests, then he will make a profit of $25 \% .$ However, as it turned out, $50 \%$ of the components were rejected. What is the loss to the manufacturer ? (in $Rs.$)

A fruit-seller buys some oranges and by selling $40 \%$ of them he fealises the cost price of all the oranges. As the oranges being to grow over-ripe, he reduces the price and sells $80 \%$ of the remaining oranges at half the previous rate of profit. The rest of the oranges being rotten are thrown away. The overall percentage of profit is

A trader sold an article at a gain of $20 \%$. Had he purchased it for $40 \%$ more and sold for $Rs.\, 24$ less, he would have incurred a loss of $20 \%$. What is the cost price (in $Rs.$) of the article?

Two toys are sold at $Rs.\,504$ each. One toy brings the dealer a gain of $12 \%$ and the other a loss of $4 \%$. The gain or loss per cent by selling both the toys is

A man purchased some eggs at $3$ for $Rs.\, 5$ and sold them at $5$ for $Rs.\, 12 .$ Thus, he gained $Rs.\, 143$ in all. The number of eggs he bought is

In these questions, two equations mabered $I$ and $II$ are given. You have to solve both the equations and mark the appropriate option.

$I.$ $2 x^{2}-11 x+15=0$

$II$. $2 y^{2}-11 y+14=0$