KBAT Problems

KBAT Problem: Comparing Two Discounts

Q: Why can't I just add 30% and 10%?

Because the second discount is taken off the already-reduced price, not the original. Thirty percent off RM600 leaves RM420, and 10% of RM420 is only RM42, not RM60. Adding the percentages assumes both act on the full RM600, which overstates the saving every time. Multiply the factors instead.

Q: How do I find the single equivalent discount?

Multiply the 'remaining' factors and subtract from one. For 30% then 10%, the factors are 0.70 and 0.90; their product 0.63 means 63% of the price remains, so 37% is the true discount. This works for any chain of successive percentage cuts, however many there are.

Q: Does the order of the two discounts matter?

For the final price, no, multiplication commutes, so 0.70 × 0.90 equals 0.90 × 0.70. Whether you take 30% then 10% or 10% then 30%, you land on the same RM378. The order only ever matters if a discount is capped at a fixed amount rather than being a straight percentage.

A KBAT problem where two discount offers must be compared, the trap is that successive percentages do not simply add.

Written by the spmmath.com.my editorial team.

Percentages do not add

One shop offers 20% then a further 10% off; another offers 30% off. The KBAT insight is that two successive discounts of 20% and 10% are not a 30% discount, apply them one after the other to see the real price.

Compute and decide

Work out the final price under each offer from the same starting price, then state which is cheaper and by how much. Showing both final prices makes the comparison, and the marks, clear.

Understand the problem

An original comparison: a jacket is priced at RM600. Offer A gives 30% off, then a further 10% off the reduced price.

Offer B gives a single 38% off. The trap is adding 30 and 10 to call Offer A '40% off'.

Successive discounts apply to a shrinking price, so they must be worked one after another, not summed.

Plan and solve

Offer A, first cut: 600 × (1 − 0.30) = 600 × 0.70 = RM420.
Offer A, second cut: 420 × (1 − 0.10) = 420 × 0.90 = RM378.
Offer B: 600 × (1 − 0.38) = 600 × 0.62 = RM372.
Compare: RM372 < RM378, so Offer B is cheaper by RM6.

Check and a variant

Check Offer A as a single factor: 0.70 × 0.90 = 0.63, so the real discount is 37%, not the 40% that adding suggests, the price RM378 confirms it (63% of 600). A twist: what single discount equals Offer A's two steps?

Since 1 − 0.63 = 0.37, it is exactly 37% off. Being able to convert two successive discounts into one equivalent percentage is the deeper skill here.

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Frequently asked questions

Why can't I just add 30% and 10%?

Because the second discount is taken off the already-reduced price, not the original. Thirty percent off RM600 leaves RM420, and 10% of RM420 is only RM42, not RM60.

Adding the percentages assumes both act on the full RM600, which overstates the saving every time. Multiply the factors instead.

How do I find the single equivalent discount?

Multiply the 'remaining' factors and subtract from one. For 30% then 10%, the factors are 0.70 and 0.90; their product 0.63 means 63% of the price remains, so 37% is the true discount.

This works for any chain of successive percentage cuts, however many there are.

Does the order of the two discounts matter?

For the final price, no, multiplication commutes, so 0.70 × 0.90 equals 0.90 × 0.70. Whether you take 30% then 10% or 10% then 30%, you land on the same RM378.

The order only ever matters if a discount is capped at a fixed amount rather than being a straight percentage.