Let, the numbers are = a, a + 2, a + 4

∴ a (a + 2)(a + 4) = 2688 ……….(1)

∴ a (a + 2) = 168 ………..(2)

From (1) and (2) we get,

⇒ a + 4 = 2688/168

⇒ a + 4 = 16

∴ the third number = 16

∴ Five times the third number = 5 × 16 = 80

CP of 100 coconuts = Rs 150

∴ CP of 2000 coconuts = Rs 150 × 2000/100

= Rs 3000

∵ SP of 1 coconut = Rs 2

∴ SP of 2000 coconuts = Rs 2 × 2000

= Rs 4000

⇒ Profit = SP – CP

= 4000 – 3000

= Rs 1000

We know the formula for simple interest-

Where:

S.I. = simple interest

P = principal

R = rate = 4%

T = time = 2 yr

80 = (P × 4 × 2)/100

P = 1000

We know the formula for compound interest-

Where

A = Amount

P = Principal

R = Rate of interest = 4%

T = Time period = 2 yr

A = (1000 × 104 × 104)/(100 × 100)

A = 1081.6

So C.I. = A – P

⇒ C.I. = 1081.6 – 1000

⇒ C.I. = 81.60

First of all, we use given quantities and place them in the formula, to know the required quantities.

Cost of 1 litre milk of 1st quality = Cost price of dearer = d = Rs. 13.70

Cost of 1 litre milk of 2nd quality = Cost price of cheaper = c = Rs. 11.90

Desired cost of 1 kg of the mixture = Mean price = m = Rs. 12.50

Time = Distance/Speed

Total time = T₁ + T₂ + T₃

⇒ Total time = 2000/40 + 1500/60 + 1500/30

⇒ Total time = 50 + 25 + 50 = 125 hrs

Average speed = (Total Distance)/(Total time)

∴ Average speed = 5000/125 = 40 km/hr

Distance = Speed × Time ⇒ Time = Distance/Speed

If two trains are going toward each other their relative speed = Sum of their speed

Here, the train and the man is running towards each other. So, the relative speed will be

= (40 + 5) kmph = 45 kmph.

= 45 × (1000/3600) m/sec

= (25/2) m/s

The length of the train = 120m

∴ The required time to pass the man = 120/(25/2) = 120 × (2/25) = 9.6 sec.

The pattern of the given series is:

⇒ 1 × 3⁰ = 1

⇒ 2 × 3¹ = 6

⇒ 3 × 3² = 27      

⇒ 4 × 3³ = 108

⇒ 5 × 3⁴ = 405 = ?

The pattern of the given series is:

⇒ 2 - 1 = 1 = 1²

⇒ 10 - 2 = 8 = 2³

⇒ 19 - 10 = 9 = 3²

⇒ 83 - 19 = 64 = 4³

⇒ ? - 83 = 5²

⇒ ? = 108