Maths

(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

(c): A + B + C = 12540 .… (1)

$A=\frac{3}{7}(B+C)$

$\frac{A}{B+C}=\frac{3}{7}$

So, A's Share = $\frac{3}{10}*12540=3762$ $\frac{}{}$

$B=\frac{2}{9}(A+C)$

$\frac{B}{A+C}=\frac{2}{9}$

So, B's Share = $\frac{2}{11}*12540=2280$

(c):Let x be the percentage of water in the resultant mixture.

Using the alligation rule, we have

$\frac{30}{25}=\frac{(40-x)}{(x-20)}$

6 (x – 20) = 5 (40 – x)

6x – 120 = 200 – 5x

11x = 320

x = $\frac{320}{11}=29.09\mathrm{\%}$

(b):Vande Bharat takes 6 hours from New Delhi to Bhopal. Duronto takes 4 hours from Bhopal to New Delhi. Let the distance between Delhi and Bhopal be 'd' kms.

Speed of Vande Bharat = $\frac{d}{6}km/hr$ $$

Speed of Duronto = $\frac{d}{4}km/hr$ $$

They will meet after = $\frac{d}{\frac{d}{6}+\frac{d}{4}}=2\frac{2}{5}hours$ $$

= 2 hours & 24 minutes

Hence, required time = (7 + 2.24)

= 9 : 24 a.m.

Factorised from = 2⁴ * 3⁴ * 5² * 7²

Total no. of factor = 5* 5 * 3 * 5

= 225 factors

113^rd factor = $\sqrt[]{N}$

 i.e. 7 * 5 * 3² * 2² = 1260