# Question

In the month December, Ali, Bala and Charlie spent a total of \$1780 altogether. In January, Ali increased his expenditure by \$150, Bala doubled his expenditure and Charlie reduced his expenditure by \$180. Their expenditures then became the same.

a) Of the three boys, who spent the most amount of money and who spent the least amount of money in December?

b) What was Bala’s expenditure in December?

c) What was Charlie’s expenditure in December?

In December, let Bala spent 1u.
A + 1u + C ——- 1780
4A + 4u + 4C ——- 1780 x 4 = 7120

In January,
(A + 150) + (2u) + (C – 180) = 6u
A – 4u + C ——- 180 – 150 = 30

5A + 5C ——- 7120 + 30 = 7150
A + C ——- 7150/5 = 1430
B or 1u ——- 1780 – 1430 = 350 b) (least) a)
A + 150 ——- 350 x 2 = 700
A ——- 700 – 150 = 650
C – 180 ——- 700
C ——- 700 + 180 = 880 c) (most) a)

Ans : a) most — Charlie, least — Bala; b) \$250; c) \$880.

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Working backwards

 A B C End (Jan) 2u let 2u 2u Af first (Dec) 2u-150 u 2u+180

(a) In Dec, Charlie spent the most and Bala spent the least

Sum all at first:  2u-150 + u + 2u+180 = 1780 –>  u=350

(b) Bala spent \$350 in December.

2u+180 = 2 x 350 +180 = 880

(c) Charlie spent \$880 in December. – sorry, corrected (thanks BigDevil…)

Checked – In Jan, each of them spent \$700.

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