SRCC GBO 2015

Cost price of house = Rs. $$C$$

Profit on house = $$\frac{25}{100}\times C=Rs.$$ $$\frac{C}{4}$$

Tax paid = $$\frac{50}{100}\times\frac{C}{4}=Rs.$$ $$\frac{C}{8}$$

=> Ans - (C)

Area of figure = area (ABCD) + area (BDE)

= $$(ab)+(\frac{1}{2}\times b\times b)$$

= $$b(a+\frac{b}{2})$$

=> Ans - (C)

Given : $$2x + y= 5$$ -------------(i)

Multiplying equation (i) by 2, we get :

=> $$4x+2y=10$$

=> Ans - (D)

Let radius of circle be $$r=1$$ units

=> Area = $$\pi r^2=\pi$$ sq.units

Now, after 6% increase, new radius = $$r'=1.06$$ units

=> New area = $$\pi(r')^2=1.1236\pi$$ sq. units

$$\therefore$$ Increase in area = $$\frac{1.1236-1}{1}\times100=12.36\%$$

=> Ans - (D)

Number of time light flashes in 6 seconds = 1 time

Number of times it will flash in 45 minutes (or 2700 sec) = $$\frac{2700}{6}=450$$

=> Ans - (C)

Let the L.C.M. and H.C.F. of the two numbers be $$x$$ and $$y$$

According to ques, => $$x+y=638$$

and $$x-y=580$$

Adding above equations, we get : $$x=609$$ and $$y=29$$

Thus, H.C.F. = 29 and L.C.M. = 609

Let the two numbers be $$29a$$ and $$29b$$, where $$a$$ and $$b$$ are co-prime

=> Sum of numbers = $$29a+29b=290$$

=> $$a+b=10$$

Since, they are co-prime, possible values of $$(a,b)$$ are : (1,9), (3,7)

Now, to get L.C.M. as 609, we have $$a=3$$ and $$b=7$$ (or vice-versa)

Thus, the numbers are : 87 and 203

=> Ans - (B)

Let the ten's digit be $$x$$ and unit's digit = $$x+3$$

Thus, number = $$10x+(x+3)=11x+3$$

If we interchange the digits, number = $$10(x+3)+x=11x+30$$

=> Difference = $$(11x+30)-(11x+3)=27$$

Since, the difference is always constant, hence we cannot find the two-digit number, it can be 14,25,36,47,58,69

=> Ans - (D)

Let the price of washing machine = Rs. $$100x$$

Rate of interest is 10% for 3 years under simple interest

=> S.I. = $$\frac{P\times R\times T}{100}$$

Total amount paid = $$3000+(3\times1300)=Rs.$$ $$6900$$

=> $$100x+\frac{(100x-3000)\times10\times3}{100}=6900$$

=> $$100x+(x-30)\times30=6900$$

=> $$130x-900=6900$$

=> $$130x=6900+900=7800$$

=> $$x=\frac{7800}{130}=60$$

$$\therefore$$ Sum = Rs. 6,000$$ and thus total interest charged = Rs. 900

=> Ans - (D)

Let the three sides be $$(a-d),a,(a+d)$$ units

In a right angled triangle,

=> $$(a-d)^2+(a)^2=(a+d)^2$$

=> $$2a^2+d^2-2ad=a^2+d^2+2ad$$

=> $$a^2=4ad$$

=> $$a=4d$$

Thus, the three sides are : $$3d,4d,5d$$

Thus, the sides are multiples of either 3,4 or 5. Thus, only possible side among the options is 56.

=> Ans - (D)

To reach R at the same moment for the first time, Sona has to gain one entire trip (Q-R, R-Q,Q-R) which is 36 km, over Mona.

Hence, the difference between distances covered by Mona and Sona in time T shall be 36 km.

This means, 60T - 45T = 36,

or T = 144 min, which is 10:24 am.