Minimum usage level required = x

    2500/x < 15

    2500 < 15x

    x> 2500/15 ⇒ x > 166.67 hours

On each of the 1200 watches that he sells in the season, he makes a profit of Rs. 100(i.e. Rs. 250 - Rs. 150). On each of the 300 (i.e. 1500 - 1200) watches that are not sold, he incurs a loss of Rs. 150, which is the manufacturing cost. His additional expense is Rs. 30,000 (given). Thus his net profit in the season is Rs. (1,20,000 - 45,000 - 30,000) = Rs. 45,000.

Since maximum rise is there
we need to assume that initially Akshay took 1 kg of pulse for every 3 kg of rice
and after price rise he takes 1/2 kg of pulse for every 3 kg of rice

now initially he eats x kg rice and x/3 kg pulse
Let akshay consumes y kg of rice after price rise so total consumption = y+y/6
x+x/3=y+y/6
y=8x/7
this will lead to 14% rise if the prices rise by equal percentage.

(a + b + c + d)2 = (4m + 1)2

Thus, a2 + b2 + c2 + d2 + 2(ab + ac + ad + bc + bd + cd) = 16m2 + 8m + 1

a2 + b2 + c2 + d2 will have the minimum value if (ab + ac + ad + bc + bd + cd) is the     maximum.

This is possible if a = b = c = d = (m + 0.25) …….since a + b + c + d = 4m + 1

In that case 2(ab + ac + ad + bc + bd + cd) = 12(m + 0.25)2 = 12m2 + 6m + 0.75      Thus, the minimum value of a2 + b2 + c2 + d2 = (16m2 + 8m + 1) – 2(ab + ac + ad +           bc + bd + cd)

= (16m2 + 8m + 1) – (12m2 + 6m + 0.75)

= 4m2 + 2m + 0.25

Since it is an integer, the actual minimum value = 4m2 + 2m + 1