X and Y enter into a partnership with capital in the ratio 3: 5. After 5 months X adds 50% of his capital, while Y withdraws 60% of his capital. What is the share (in lakhs) of X in the annual profit of 6.84 lakhs?

If the radius of the base of a right circular cylinder is increased by 20% and the height is decreased by 30%, then what is the percentage increase/decrease in the volume?

On selling an article for ₹123.40, the gain is 20% more than the amount of loss incurred on selling it for ₹108. If the article is sold for ₹120.75, then what is the gain/loss per cent?

If $${45\over53}={1\over{a+{1\over b+{1\over c-{2\over 5}}}}}$$  , where a, b and c are positive integers, then what is the value of (4a-b+3c)?

In ∆ABC, ∠C=90⁰, Point P and Q are on the sides AC and BC, respectively, such that  AP:PC=BQ:QC=1:2.Then, $${AQ^2+BP^2}\over AB^2$$  is equal to:

If sin 3A=cos(A+10⁰), where 3A is an acute angel, then what is the value of $$2cosec{3A\over2}+6sin^23A-{3\over 2}tan^2\ 3A$$?

The value of   $${cosec^230^0sin^245^0+sec^260^0}\over {tan60^0cosec^245^0-sec^260^0tan45^0}$$ is 

cosA(sec A – cosA)(cotA+tanA)=?