Maths

(a):Let us suppose the income of man = Rs. 1000

Savings = 15% of 1000 = Rs. 150

Expenditure = 1000 – 150 = 850

New Income = 1.2 * 1000 = 1200

New Expenditure = 1.1 * 850 = 935

New Savings = 1200 – 935 = 265

Required percentage = $\frac{265}{1200}*100=22.08\mathrm{\%}$

(c):Total number of factors of factors of 756 = 22 * 33 * 7 = (2 + 1) (3 + 1) (1 + 1) = 24

So, total sets are $\frac{24}{2}=12.$

(a):Cost of material = 30% of 4000 = 1200

New cost of material = $\frac{\frac{}{}}{}$ $1200\left(1?\frac{\frac{26}{6}}{100}\right)$ = 1150

Cost of manufacturing = $2000\left(1+\frac{20}{100}\right)$ $\frac{}{}$ = 2400

So, new profit = 4000 – (2400 + 1150) = 450

(b):We have to find last non zero digit by 4 so we will eliminate 0 in question so now it becomes 104⁷²³ = 4 as 4^odd = 4

(a):We have (A ¬ 20) = 0.4 (B + 20), i.e. A – 0.4B = 28

And (B – 40) = 0.4 (A + 40), i.e. B – 0.4A = 56

Solve these equation's we get A = 60 Rs.

(b):In normal time rate = Rs. 6 per hour

During sale rates are increased by 50% i.e.,

Rate 40-hour week = 240 + 50% of 240 = Rs. 360

Rate per hour = Rs. 9 per hour

Now, according to the question,

Required commission = 9 * 60 = Rs. 540

(c):The digit sum of factorial of numbers till 5! is 9. 6! onwards each factorial will have digit sum as 9

(a):From the problem, we have

CP $CP*\frac{125}{100}=360$

CP = 72 * 4 = Rs.288

If the same item is sold for Rs.260, there will be a loss of Rs. 288 – Rs. 260 = Rs. 28

Let weight of body by fourth experiment = x

Net total of seven experiments = 53.735 * 7

= 376.145 gms.

Net total of first three = 3 * 54.005 = 162.015 gms.

Net total of 6th & 7th = 2 * 53.991 = 107.982 gms.

W5 + W4 = (x + 0.004) + x = 2x + 0.004

162.015 + 2x + 0.004 + 107.982 = 376.145

x = 53.072 gms