Question

A 700g dry fruit pack costs Rs 72. It contains some cashew kernels and the rest as dry grapes. If cashew kernels cost Rs 96 per kg and dry grapes costs Rs 112 per kg, what were the quantities of the two dry fruits separately.

Answer 1

Let quantities of cashew kernels and fry grapes be x and y respectively.
Therefore,
x + y = 700g
⇒ y = 700 - x   .......(i)
Cost of cashew kernels

= ${\displaystyle \frac{96}{\text{kg}}}$

= ${\displaystyle \frac{0.096}{\text{g}}}$

Cost of dry grapes

= Rs.${\displaystyle \frac{112}{\text{kg}}}$

⇒ ${\displaystyle \frac{0.112}{\text{g}}}$

Cost  of dry fruit pack = Rs.72
Therefore,
0.096 x + 0.112y = 72 .......(ii)
Substituting (i) in (ii)
0.096x + 0.112(700 - x) = 72
⇒ 0.096x + 78.4 - 0.112x = 72
⇒ 0.016x = 6.4
⇒ x = 400
Substituting value of x in (i)
400 + y = 700
⇒ y = 300
Therefeore, cashew kernels = 400g and dry grapes = 300g.