PSLE
Xylia and Tom bought durians at the prices shown below.

3 Large durians for $12
4 Small durians for $6

1. Xylia bought an equal number of large and small durians. She spent $90 more on the large ones. How many durians did she buy altogether?
2. Tom spent an equal amount of money on the large and small durians. What fraction of the durians he bought were small?

(a)
Number of large and small durians that Xylia bought is the same. Make the number of large and small durians the same. LCM of 3 and 4 is 12.

Cost of 3 large durians = $12
Cost of 12 large durians = 4 x 12 = $48

Cost of 4 small durians = $6
Cost of 12 small durians = 3 x 6 = $18

Difference in the cost of buying 12 small durians and 12 large durians
= 48 - 18
= $30

Number of sets of durians
= 90 ÷ 30
= 3

Number of durians that Xylia bought
= 3 x 2 x 12
= 72

(b)
Tom spent an equal amount of money on the large and small durians. Make the amount of money spent on the large and small durians the same.
LCM of 12 and 6 is 12.

Number of large durians that Tom bought
= 3 x (12 ÷ 12)
= 3 x 1
= 3

Number of the small durians that Tom bought
= 4 x (12 ÷ 6)
= 4 x 2
= 8

Fraction of the durians that Tom bought that were small
= ⁸_{3 + 8}
= ⁸₁₁

Answer(s): (a) 72; (b) ⁸₁₁