The L.C.M and H.C.F of the two numbers are 84 and 21 respectively. If the numbers have a ratio of 1: 4, what is the larger number?

What is the area of an equilateral triangle having altitude equal to $$5\sqrt{3}$$cm.

The graphs of the equations 3x-20y-2=0 and 11x-5y+61=0 intersect at P(a,b). What is the value of (a² + b² — ab)/(a² — b² + ab)?

The LCM of two numbers is 864 and their HCF is 144. If one of the numbers is 288, the other number is:

Find the cube root of $$ ^{3}\sqrt{-13824}$$.

Pipes A and B together can fill a tank in 16 hours, whereas pipe C alone can empty the full tank in 24 hours. A and B were opened together for 10 hours and then closed. Pipe C was then opened. The tank will now be emptied by C in:

Study the given graph and answer the question that follows.

If 60% of the total number of students obtaining 50 marks or more but less than 70 marks are girls and 55 % of the total number of students obtaining 70 marks or more but less than 90 marks are also girls. Then the total number of girls obtaining 50 marks or more but less than 90 marks is:

A shopkeeper bought 25 kg. of pulses at the rate of Rs. 54 kg. He sold forty percent of the total quantity at the rate of Rs. 50 per kg. at what price per kg should he sell the approximately quantity to make 25% overall profit ?