Question 11

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?

Let's say amount of fertilizer alpha taken be $$a$$ units.

Amount of fertilizer beta taken be $$b$$ units.

Now, ratio of K in alpha = 10% and in final mixture, the ratio is 6%

So,$$\dfrac{10}{100}\times\ a+0=\dfrac{6}{100}\times\ \left(a+b\right)$$

or,Β $$0.1a=0.06a+0.06b$$

or,Β $$0.1a-0.06a=0.06b$$

or,Β $$0.04a=0.06b$$

or,Β $$\dfrac{a}{b}=\dfrac{6}{4}=\dfrac{3}{2}$$

So, let say $$a=3$$ and $$b=2$$

Let say percentage of P in Beta be $$p%$$

So,Β $$3\cdot\dfrac{70}{100}+2\cdot\dfrac{p}{100}=5\cdot\dfrac{68}{100}$$

or,Β $$210+2p=340$$

or,Β $$p=\dfrac{340-210}{2}=\dfrac{130}{2}=65\%$$

So, percentage of P in Beta = $$65\%$$

So, percentage of N in beta =Β $$\left(100-65\right)\%=35\%$$

So, correct answer is option C.

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