Ratios & Proportion

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An outgoing batch of students wants to gift a PA system worth Rs 4,200 to their school. If the teachers, offer to pay $50\%$ more than the students and an external benefactor gives three times the teacher's contribution, then how much should the teachers donate?


Rs 600


Rs 840


Rs 900


Rs 1,200

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Option(C) is correct

The ratio of the share students : teacher: benefactor=$1:1.5:4.5$

So the proportion to teacher's share = \(\dfrac{1.5}{7}\)

Hence, the teachers would donate \(\dfrac{1.5}{7}\times 4200= \text{Rs }900\)

Edit: Thank you Deepak for explaining the final ratio in the comments.

Edit 2: for an alternate approach, check comment by Zoha Amjad.

(12) Comment(s)

Zoha Amjad

S+ (150/100*S)+ 3*(150/100*S) = 4200

S= 600

so teachers contribution will be 150% of 600 = 900


Unfortunately I took it as "Rs 50"

They should avoid general language

Be specific.


Oh sorry

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If teacher gives rs 900 ...so the benefactor will give 2700rs and the students rs 850 .....the total is not rs 4200 ....please explain ..


Students will donate Rs. 600, teacher will donate Rs. $1.5 \times 600 = 900$ And external benefactor wil donate Rs. $900 \times 3 =2700$.

If you sum these all, $=600+900+2700=4200$. Which is the given total in the question. So everything matches.

You have miscalculated the donation given by students.


Such a quick response, you guys are doing a really wonderful job here. Cheers.


how did this ratio come out


it's easy, say student wants to gift Rs. $100$.

Then from the question, the teachers, offer to pay $50$ more than the students.

Thus teacher $=150$.

Again, an external benefactor gives three times the teacher's contribution $=150 \times 3 = 450$

Thus, ratio becomes,

students : teacher: benefactor $=100:150:450$ or $1:1.5:4.5$


And teacher's share is calculated using this formula,

proportion to teacher's share $=\dfrac{1.5}{1+1.5+4.5}=\dfrac{1.5}{7}$


I think... The question should be like "outgoing batch of students, teachers and beneficiaries want to gift a pa of worth 4200" but not merely students give a gift of worth 4200..

Excuse me, if I wrong.



Ramesh Sidhdhant

Good question.

Great attempt...

You are doing a nice job.

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