One quality of wheat at Rs. 9.30 per kg is mixed with a higher quality wheat in the ratio 8 ∶ 7. If the mixture so formed costs Rs. 10 per kg, what is the rate per kg of the second quality of wheat?
One quality of wheat at Rs. 9.30 per kg is mixed with a higher quality wheat in the ratio 8 ∶ 7. If the mixture so formed costs Rs. 10 per kg, what is the rate per kg of the second quality of wheat?
1). Rs. 10.30
2). Rs. 10.60
3). Rs. 10.80
4). Rs. 11
1 answers
Cost of 1 kg wheat of 1st quality = Cost price of cheaper = c = Rs. 9.30
Cost of 1 kg wheat of 2nd quality = Cost price of dearer = d = Rs. x (suppose)
Cost of 1 kg of the mixture = Mean price = m = Rs.10
By formula,
$(\begin{array}{l} \frac{{Quantity\;of\;Cheaper}}{{Quantity\;of\;Dearer}} = \frac{{d - m}}{{m - c}}\\ \Rightarrow \frac{{Quantity\;of\;Cheaper}}{{Quantity\;of\;Dearer}} = \frac{{x - 10}}{{10 - 9.30}} = \\ \frac{8}{7} \Rightarrow \frac{{x - 10}}{{0.70}} = \frac{8}{7} \end{array})$
⇒ 7x – 70 = 8 × 0.70
⇒ 7x = 5.6 + 70
⇒ 7x = 75.6
⇒ x = Rs. 10.8
∴ The rate of the second quality of wheat is Rs. 10.80 per kg.