Easy does it! The Smart Scholar Method

Let the weights be a, b, c, d and e (Not necessarily in the order Asha, Bina, Chitra, Diana and Esha) and let a < b < c < d < e.

The sum of the weights of the lightest two should be 150.

That is, a + b= 150                                                                        … … (1)

The sum of the weights of the heaviest two should be 161.

That is, d + e = 161                                                                       … … (2)

The sum of all the 10 numbers = 1556

That is, 4*(a + b + c + d + e) = 1556

Or (a + b + c + d + e) = 389                                                          … ...  (3)

(3) – (1) – (2) gives c = 78                                                              ... ...  (4)

It can be inferred that c + e = 160

This implies that  e= 120 – c = 160 – 78 = 82                                ... ...  (5)

From (2) and (5), d = 79.

Since a + c must be equal to 142, (4) implies that a= 74.

From (1) above, b= 76.

The weights of the five girls are 74, 76, 78, 79 and 82 kgs. As Chitra is the heaviest, she weighs 82 kgs.

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