Question

Alpha and Beta are two chemical fertilizers. Alpha consists of N, P, K and Beta consists of N and P. A mixture of Alpha and Beta is prepared in which the ratio of N, P and K is 26%, 68% and 6%. The ratio of N, P, K in Alpha is 20%, 70% and 10%. What is the ratio of N and P in Beta?

Accepted Answer

C. Let $a$ units of Alpha and $b$ units of Beta be taken. K comes only from Alpha. K in Alpha is $10\%$ and K in mixture is $6\%$. $$10\% 	imes a = 6\% 	imes (a + b) \implies 0.04a = 0.06b \implies \frac{a}{b} = \frac{3}{2}$$ Let $a = 3$ and $b = 2$. Let percentage of P in Beta be $p\%$. P in mixture: $$3 	imes 70\% + 2 	imes p\% = 5 	imes 68\%$$ $$210 + 2p = 340 \implies 2p = 130 \implies p = 65\%$$ Since Beta contains only N and P, N in Beta = $100\% - 65\% = 35\%$. Ratio of N and P in Beta = $35\%$ and $65\%$.

Chemical Fertilizer Mixture Ratio

Explanation

Practise this under exam conditions