SRCC GBO 2015

Principal sum = Rs. 800

Rate of interest = 5% for 3 years

Amount under compound interest = $$P(1+\frac{r}{100})^T$$

= $$800\times(1+\frac{5}{100})^3$$

= $$800\times(\frac{21}{20})^3$$

= $$\frac{9261}{10}=Rs.$$ $$926.10$$

=> Ans - (C)

Let principal amount be Rs. $$P$$

Rate of interest = 5% for 3 years

Compound interest = $$P[(1+\frac{R}{100})^T-1]$$

=> $$P[(1+\frac{5}{100})^3-1]=63.05$$

=> $$P[(\frac{21}{20})^3-1]=63.05$$

=> $$P\times(\frac{9261-8000}{8000})=63.05$$

=> $$P=63.05\times\frac{8000}{1261}=Rs.$$ $$400$$

=> Ans - (A)

Let time taken by B = $$t$$ days, and thus time taken by A = $$(t-60)$$ days

Since, efficiency is inversely proportional to time,

=> $$\frac{3}{1}=\frac{t}{t-60}$$

=> $$3t-180=t$$

=> $$2t=180$$

=> $$t=\frac{180}{2}=90$$

Thus, time taken by B is 90 days and by A is 30 days

=> Time taken by them to finish the work together = $$1\div(\frac{1}{90}+\frac{1}{30})$$

= $$\frac{90}{4}=22\frac{1}{2}$$ days

=> Ans - (B)

Let B's efficiency = $$4x$$ units/days

=> A's efficiency = $$2x$$ units/day

=> C's efficiency = $$3x$$ units/day

If C alone can finish the work in 40 days, => Total work = $$120x$$ units

Time taken for all of them to finish the work together = $$\frac{120x}{(4x+2x+3x)}$$

= $$\frac{120}{9}=13\frac{1}{3}$$ days

=> Ans - (A)

Speed of train = 58 km/hr and speed of passer by = 4 km/hr

Relative speed = $$58-4=54$$ km/hr = $$54\times(\frac{5}{18})=15$$ m/s

=> Time taken to cross the passer by = $$\frac{110}{15}=7\frac{1}{3}$$ seconds

=> Ans - (C)

Distance covered by car in 10 hours at 48 km/hr

= $$10\times48=480$$ km

Now, speed when it is covered in 8 hours = $$\frac{480}{8}=60$$ km/hr

Thus, speed must be increased by = $$60-48=12$$ km/hr

=> Ans - (C)

Let time taken by B is $$t$$ minutes, and thus time taken by A = $$(t+20)$$ minutes

Also, speed is inversely proportional to time,

=> $$\frac{3}{4}=\frac{t}{t+20}$$

=> $$3t+60=4t$$

=> $$t=60$$

Thus, time taken by A = $$60+20=80$$ minutes = $$1\frac{1}{3}$$ hours

=> Ans - (B)

Let distance each side be $$d$$ km

Using, time = distance/speed

=> $$\frac{d}{8}+\frac{d}{6}=3.5$$

=> $$\frac{7d}{24}=\frac{7}{2}$$

=> $$d=12$$ km

Thus, total distance travelled (both sides) = $$12\times2=24$$ km

=> Ans - (C)

Let Aman's age = $$3x$$ years and his mother's age = $$11x$$ years

=> Difference = $$11x-3x=8x=24$$

=> $$x=3$$

$$\therefore$$ Ratio after 3 years = $$\frac{3(3)+3}{11(3)+3}$$

= $$\frac{12}{36}=1:3$$

=> Ans - (A)

Let amount with A, B and C be Rs. $$300,400,500$$ respectively.

First, B gives $$\frac{1}{4^{th}}$$ to A and $$\frac{1}{4^{th}}$$ to C

=> Amount with A = $$300+\frac{1}{4}\times400=Rs.$$ $$400$$

C = $$500+\frac{1}{4}\times400=Rs.$$ $$600$$

B = $$400-100-100=Rs.$$ $$200$$

Secondly, C gives $$\frac{1}{6^{th}}$$ to A

=> Amount with A = $$400+\frac{1}{6}\times600=Rs.$$ $$500$$

B = $$Rs.$$ $$200$$

C = $$600-100=Rs.$$ $$500$$

Thus, final ratio with A:B:C = 5:2:5

=> Ans - (D)