UKMT - Intermediate Mathematical Challenge - 2023 - 11 | Exact Science

11

Jill was given a large jar of jam. She gave one sixth of the jam to Jan. Jill then gave one thirteenth of the remaining jam to Jas. Jill was left with 1 kg of jam.

What was the weight, in kg, of the jam in Jill’s jar at the start?

A. 1.2

B. 1.3

C. 1.4

D. 1.6

E. 1.9

Answer

B. 1.3

SOLUTIOn

After giving away one sixth of the jam and then one thirteenth of the remaining jam, Jill was left with twelve thirteenths of five sixths of the original weight of jam.

Now 12/13 × 5/6 = 60/78 = 10/13. So ten thirteenths of the original weight of jam was 1 kg.

Hence Jill had 1.3 kg of jam in the jar at the start.

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