LCM(8,12,18) = 72 minutes. 9:00 AM + 72 minutes = 10:12 AM.
HCF(56,72) = 8. x must be multiple of 8 and have HCF with 56,72 as 8. Largest multiple of 8 < 100 is 96.
Let CP = x. SP₁ = 1.15x. SP₂ = 1.25x = 1.15x + 100. 0.1x = 100. x = 1000.
Relative speed = 50+70 = 120 km/h = 100/3 m/s. Distance = 100+100 = 200m. Time = 200÷(100/3) = 6 seconds.
Net rate = 1/10 + 1/15 + 1/20 - 1/30 = 6/60 + 4/60 + 3/60 - 2/60 = 11/60. Time = 60/11 ≈ 5.45, closest is 6.
Downstream = 60/4 = 15 km/h. Upstream = 60/6 = 10 km/h. Speed in still water = (15+10)/2 = 12.5 km/h.
HCF×LCM = number1×number2. 12×288 = 48×other. Other = 3456/48 = 72.
12100 = 10000(1+r)². (1+r)² = 1.21 = (1.1)². r = 10% p.a.
When successive discounts are applied, each discount is calculated on the remaining amount after the previous discount. We can find the equivalent single discount using the formula for compound discounts.
Step 1: Apply the first discount of 20%
If the marked price is \(MP\), after a 20% discount, the remaining price is:
Step 2: Apply the second discount of 15% on the reduced price
The second discount of 15% is applied to \(P_1\):
Step 3: Calculate the combined multiplier
This means the customer pays 68% of the marked price.
Step 4: Find the equivalent single discount
The equivalent single discount is the percentage reduction from the original price:
For successive discounts, use:
Equivalent Discount=a+b−
100
ab
where
a=20% and b=15%
=20+15−
100
20×15
=35−3
=32%
Therefore, the equivalent single discount is 32%.
Answer: The equivalent single discount is \(32\%\) (Option A)
Net rate = 1/10 + 1/15 - 1/20 = 6/60 + 4/60 - 3/60 = 7/60; Time = 60/7 ≈ 8.57 hours
