A vessel contains 28 liters of honey and water solution with honey and water ratio 4 : 3.21 liters of honey-water solution is added to this that his honey to water ratio as 2 : 1. Again a 51 liters honey-water solution that has honey to water ratio as 9 : 8 is added to this. After this, 10 liters of the solution is replaced with pure honey. What is ratio of water to honey in the final mixture?

Created: 3 months ago | Updated: 3 months ago

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প্রশ্নে বলা হচ্ছে, একটি পাত্রে 4 : 3 অনুপাতে 28 লিটারের মধু ও পানির মিশ্রণ রয়েছে। ঐ পাত্রে আরো 21 লিটার মিশ্রণ যোগ করায় মধু ও পানির অনুপাত হলো 2 : 1. এরপর আবার 9 : 8 অনুপাতে থাকা 51 লিটারের মধু ও পানির মিশ্রণ ঐ পাত্রে ঢালা হল। এরপর সমগ্র মিশ্রণ হতে 10 লিটার মিশ্রণ মধু দ্বারা Replace করা হল। সবশেষে ঐ পাত্রে পানি ও মধুর অনুপাত কত ছিল?

We will find out honey and water from three different ways.

We get total amount of honey from three solution,

= $= [(28 \times \frac{4}{7}) + (21 \times \frac{3}{22}) + (51 \times \frac{9}{17})] = 16 + 14 + 27 = 57 l i t e r s A n d w e g e t t o t a l a m o u n t o f w a t e r f r o m t h r e e s o l u t i o n, = [(28 \times \frac{3}{7}) + (21 \times \frac{1}{3}) + (51 \times \frac{8}{17})] = 12 + 7 + 24 = 43 l i t e r s ∴ T h e a m o u n t o f t o t a l s o l u t i o n = 57 + 43 = 100 l i t e r s . H e r e, 10 l i t e r s o f p u r e h o n e y i s 10 % o f 100 l i t e r s o f s o l u t i o n . S o, t h i s 10 % s o l u t i o n w i l l b e r e p l a c e d f r o m b o t h h o n e y a n d w a t e r w i t h 10 l i t e r s p u r e h o n e y . ∴ T h e a m o u n t o f h o n e y a f t e r r e p l a c e m e n t = [57 - (10 % o f 57) + 10] = 67 - 5.7 = 61.3 l i t e r s A n d t h e a m o u n t o f w a t e r a f t e r r e p l a c e m e n t = [43 - (10 % o f 43) + 10] = 43 - 4.3 = 38.7 l i t e r s ∴ W a t e r : H o n e y = 38.7 : 61.3 = 387 : 613 [M u l t i p l y i n g b y 10] A n s w e r : 387 : 613 .$

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