A trader sells 10 litres of a mixture of paints A and B, where the amount of B in the mixture does not exceed that of A. The cost of paint A per litre is Rs. 8 more than that of paint B. If the trader sells the entire mixture for Rs. 264 and makes a profit of 10%, then the highest possible cost of paint B, in Rs. per litre, is

In a circle with centre $O$ and radius $1$ cm, an arc $AB$ makes an angle $60^\circ$ at $O$. Let $R$ be the region bounded by the radii $OA$, $OB$ and the arc $AB$. If $C$ and $D$ are two points on $OA$ and $OB$, respectively, such that $OC = OD$ and the area of triangle $OCD$ is half that of $R$, then the length of $OC$, in cm, is

If $f(x + 2) = f(x) + f(x + 1)$ for all positive integers $x$, and $f(11) = 91$, $f(15) = 617$, then $f(10)$ equals.

The distance from $A$ to $B$ is $60$ km. Partha and Narayan start from $A$ at the same time and move towards $B$. Partha takes four hours more than Narayan to reach $B$. Moreover, Partha reaches the mid-point of $A$ and $B$ two hours before Narayan reaches $B$. The speed of Partha, in km per hour, is

A CAT aspirant appears for a certain number of tests. His average score increases by $1$ if the first $10$ tests are not considered, and decreases by $1$ if the last $10$ tests are not considered. If his average scores for the first $10$ and the last $10$ tests are $20$ and $30$, respectively, then the total number of tests taken by him is

Two types of tea, $A$ and $B$, are mixed and then sold at Rs. $40$ per kg. The profit is $10\%$ if $A$ and $B$ are mixed in the ratio $3 : 2$, and $5\%$ if this ratio is $2 : 3$. The cost prices, per kg, of $A$ and $B$ are in the ratio

A wholesaler bought walnuts and peanuts, the price of walnut per kg being thrice that of peanut per kg. He then sold $8$ kg of peanuts at a profit of $10\%$ and $16$ kg of walnuts at a profit of $20\%$ to a shopkeeper. However, the shopkeeper lost $5$ kg of walnuts and $3$ kg of peanuts in transit. He then mixed the remaining nuts and sold the mixture at Rs. $166$ per kg, thus making an overall profit of $25\%$. At what price, in Rs. per kg, did the wholesaler buy the walnuts?

When they work alone, $B$ needs $25\%$ more time to finish a job than $A$ does. They two finish the job in $13$ days in the following manner: $A$ works alone till half the job is done, then $A$ and $B$ work together for four days, and finally $B$ works alone to complete the remaining $5\%$ of the job. In how many days can $B$ alone finish the entire job?

Given an equilateral triangle $T_1$ with side $24$ cm, a second triangle $T_2$ is formed by joining the midpoints of the sides of $T_1$. Then a third triangle $T_3$ is formed by joining the midpoints of the sides of $T_2$. If this process of forming triangles is continued, the sum of the areas, in sq cm, of infinitely many such triangles $T_1, T_2, T_3, \ldots$ will be

While multiplying three real numbers, Ashok took one of the numbers as $73$ instead of $37$. As a result, the product went up by $720$. Then the minimum possible value of the sum of squares of the other two numbers is: