Abhinav purchased a certain number of pencils and a certain number of pens spending 15 on the whole. If each pen costs him 24 and each pencil 21, then how many pens and pencils could he have bought

Assuming he spent 150 on the total purchase (though you have mentioned 15), the equation that can be formed is 24x+21y=150, cancelling out the factor 3, we get 8x+7y=50, the integral solution of this is 1,6 i.e., 1 pen and 6 pencils, so a total of 7. Hope that helps.