PSLE
Diana and Fred bought durians at the prices shown below.

2 Large durians for $18
5 Small durians for $12

1. Diana bought an equal number of large and small durians. She spent $198 more on the large ones. How many durians did she buy altogether?
2. Fred 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 Diana bought is the same. Make the number of large and small durians the same. LCM of 2 and 5 is 10.

Cost of 2 large durians = $18
Cost of 10 large durians = 5 x 18 = $90

Cost of 5 small durians = $12
Cost of 10 small durians = 2 x 12 = $24

Difference in the cost of buying 10 small durians and 10 large durians
= 90 - 24
= $66

Number of sets of durians
= 198 ÷ 66
= 3

Number of durians that Diana bought
= 3 x 2 x 10
= 60

(b)
Fred 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 18 and 12 is 36.

Number of large durians that Fred bought
= 2 x (36 ÷ 18)
= 2 x 2
= 4

Number of the small durians that Fred bought
= 5 x (36 ÷ 12)
= 5 x 3
= 15

Fraction of the durians that Fred bought that were small
= ¹⁵_{4 + 15}
= ¹⁵₁₉

Answer(s): (a) 60; (b) ¹⁵₁₉