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Mixture and Alligation #25

25. Rs.460 was divided among 41 boys and girls such that each boy got Rs.12 and each girl got Rs.8. What is the number of boys?
A. 30B. 28
C. 33D. 36

Answer: Option C

Explanation:

Solution 1

Assume that the number of boys = b and number of girls = g

number of boys + number of girls = 41
=> b + g = 41 ...(1)

Given that each boy got Rs.12 and each girl got Rs.8. Then the total amount is Rs.460
=> 12b + 8g = 460 ...(2)

Now we need to solve these equations to get b and g.

(1) × 8 => 8b + 8g = 8 × 41 = 328 ...(3)
(2) - (3) => 4b = 460 - 328 = 132
=> b $=\dfrac{132}{4}=33$


Solution 2

Given that amount received by a boy = Rs.12,
Amount received by a girl =Rs.8

Total amount = 460

Given that number of boys + number of girls = 41
Hence, mean amount $=\dfrac{460}{41}$

By rule of alligation,
Amount received
by a boy (12)
Amount received
by a girl(8)
Mean amount
$\dfrac{460}{41}$
$\dfrac{460}{41}-8=\dfrac{132}{41}$$12-\dfrac{460}{41}=\dfrac{32}{41}$

Number of boys : Number of girls
=$\dfrac{132}{41}:\dfrac{32}{41}=132:32\\=66:16=33:8$

Given that number of boys + number of girls = 41

Hence number of boys $=41 × \dfrac{33}{41} = 33$

Comments(1)

profileSubhankar Roy
2016-06-27 05:44:47 
If there were 41 boys present, then total amount was = 12 * 41 = 492
Again if there were 41 girls present, then total amount was = 8 * 41 = 328

But the actual amount was 460
So now from the rule of alligation   

492      328
      460
132      32

So the ratio of boys and girls is 132:32 = 33:8
So the no. of boys are 33
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