UP SI MATHS QUIZ-38

4. Find the value of $a$ and $b$ in the following equation $\frac{5+\sqrt{3}}{7-4 \sqrt{3}}= a+\sqrt{3} b$

The ratio of chairs to tables in an office is $9: 7$ If there are 42 more chairs than tables, find the number of chairs in the office.

A solid piece of iron in the form of a cuboid of dimensions $24.5 \mathrm{~cm} \times 16.5 \mathrm{~cm} \times 12 \mathrm{~cm}$, is melted to form a solid sphere. What is the radius (in $\mathrm{cm}$ ) of the sphere? $\left(\right.$ Use $\left.\pi=\frac{22}{7}\right)$

5 men and 6 women can earn Rs. 10,500 in 6 days. 8 men and 12 women can earn Rs. 24,800 in 8 days. In how many days will 7 men and 10 women earn Rs. $26,500 ?$

An article is sold at a profit of $13 \frac{1}{4} \%$. Had it been sold for Rs. $76.70$ more, the profit would have been $16 \frac{1}{5} \%$. The cost price of the article is:

A bowler plays 75 matches and takes 60 wickets at an average of 25. In the new season, he plays 25 matches, gives 750 runs and takes 15 wickets. Find what is his new average?

240 persons went to a picnic. In this, the number of males is 20 more than the number of females and the number of adults is 20 more than the number of children. How many men are there in the picnic?

An alloy contained $42 \%$ silver. If the amount of silver in the alloy was 147 grams, then what was the amount of other elements in the alloy?

Two horses cover the same distance at the speed of $10 \mathrm{~km} / \mathrm{hr}$ and $15 \mathrm{~km} / \mathrm{hr}$ respectively. If the second horse takes 12 minutes longer than the first, then the distance covered was.