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Mathematics

A 700 g dry fruit pack costs ₹ 432. It contains some almonds and the rest cashew kernel. If almonds cost ₹ 576 per kg and cashew kernel cost ₹ 672 per kg, what are the quantities of the two dry fruits separately?

Linear Equations

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Answer

Let the quantity of almonds be x gm and that of cashew kernel be y gm.

∴ x + y = 700

⇒ x = 700 - y ……………….(1)

Cost of almonds = ₹576 per kg

Cost of x gm almonds = 5761000x\dfrac{576}{1000}x

Cost of cashew kernel = ₹672 per kg

Cost of y gm cashew kernel = 6721000y\dfrac{672}{1000}y

Cost of dry fruit pack = ₹432.

∴5761000x+6721000y=432⇒576x+672y1000=432⇒576x+672y=432000………………….(2)\therefore \dfrac{576}{1000}x + \dfrac{672}{1000}y = 432\\[1em] \Rightarrow \dfrac{576x + 672y}{1000} = 432\\[1em] \Rightarrow 576x + 672y = 432000 ………………….(2)

Substituting the value of x from equation (1) in (2) we get,

⇒ 576(700 - y) + 672y = 432000

⇒ 403200 - 576y + 672y = 432000

⇒ 403200 + 96y = 432000

⇒ 96y = 432000 - 403200

⇒ 96y = 28800

⇒ y = 2880096\dfrac{28800}{96}

⇒ y = 300.

Substituting the value of y in equation (1), we get :

⇒ x = 700 - y = 700 - 300 = 400.

Hence, almonds = 400 gm and cashew kernel = 300 gm in dry fruits pack.

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