Maharashtra Board Solutions for Exercise 3: Practice Set 12.2

The denominator of a fraction is greater than its numerator by $12$. If the numerator is decreased by $2$ and the denominator is increased by $7$, the new fraction is equivalent with $\frac{1}{2}$. If the fraction is $\frac{a}{b}$. Find $a+b$

The ratio of weights of copper and zinc in brass is $13:7$. Find the weight of zinc in a brass utensil weighing $700 \mathrm{gm}$. Give the answer in $\mathrm{gm}.$

In a two-digit number, the digit at the ten’s place is twice the digit at units’s place. If the number obtained by interchanging the digits is added to the original number, the sum is $66$. Find the number.

Of the three consecutive natural numbers, five times the smallest number is $9$ more than four times the greatest number, find the numbers.

Of the three consecutive natural numbers, five times the smallest number is $9$ more than four times the greatest number, find the greatest number.

Raju sold a bicycle to Amit at $8\%$ profit. Amit repaired it spending $₹54$. Then he sold the bicycle to Nikhil for $₹1134$ with no loss and no profit. Find the cost price of the bicycle for which Raju purchased it. Give the answer in $₹$.

A Cricket player scored $180$ runs in the first match and $257$ runs in the second match. Find the number of runs he should score in the third match, so that the average of runs in the three matches be $230$.

Sudhir’s present age is $5$ more than three times the age of Viru. Anil’s age is half the age of Sudhir. If the ratio of the sum of Sudhir’s and Viru’s age to three times Anil’s age is $5:6$ and the Viru’s age is $x$ years, then find the value of $x$.