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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. 30 | B. 28 |

C. 33 | D. 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 $=\dfrac{132}{4}=33$

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 $=41 × \dfrac{33}{41} = 33$

Subhankar 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

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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