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Candidates of four schools appear in a mathematics test. The data were as follows:

Schools | No. of candidates |
Average score |

1 | 60 | 75 |

2 | 48 | 80 |

3 | N A | 55 |

4 | 40 | 50 |

If the average score of the candidates of all the four schools is 66, find the number of

candidates that appeared from school 3.

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#### Solution

Let no. of candidates appeared from school 3 = x.

Schools | No.of candidates |
Average score |

1 | 60 | 75 |

2 | 48 | 80 |

3 | x | 55 |

4 | 40 | 50 |

Given, average score of all school = 66.

⇒ `(N_1barx_1 +N_2barx_2 + N_3barx_3 + N_4barx_4 )/(N_1 +N_2 + N_3 + N _4) = 66`

⇒ `(60+ 75 + 48 +80 + x xx 55 +40 xx 50)/(60 + 48 + x +40)= 66`

⇒`(4500 + 3840 + 55x + 2000)/148 + x`

⇒`(10340 + 55x)/(148 + x) = 66`

⇒ 10340 + 55x = 66x + 9768

⇒ 10340 + 9768 = 66x - 55x

⇒ 11x = 572

⇒ `x = 572/11`= 52

∴ No. of candidates appeared from school (3) – 52.

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