Quant Mix Quiz-4 IBPS PO 2016-17 (Plus the solutions)

1. A burger joint expected to earn profit of 40% by selling each burger at marked price. But due to some accident 16% of the burgers were completly damaged thus could not be sold, 24% slightly damaged thus sold at 80% of the cost price and remaining 60% were sold at marked price. Find the profit% in the whoe consignment ?

A. 4.8%
B. 3.6%
C. 3.2%
D. 5.6%
E. None of these

Sol. Lets assume total number of burgers be 100.
Cost of each burger be c.p.
Marked price of each burger be m.p.

As given that 40% profit for each burger at m.p. thus,

40/100 = (m.p.-c.p.)/c.p.

m.p.= (7/5)c.p.

Now total selling price after the accident,

= (16*0*m.p.)+(24*0.8*c.p.)+(60*1*m.p.)

= 19.2c.p + 60m.p.

Now profit % will be,

= 100*[(19.2c.p + 60m.p.)-100c.p.]/100c.p.

= 3.2 %

2. In 2016, age of suresh and ramesh is in the ratio 4:5. In 2006, suresh's age was half of his age at 2016 and ramesh's age was 3/5th of his age at 2016. Find the age of suresh in 20126 ?

A. 30 yrs 
B. 25 yrs
C. 20 yrs
D. 40 yrs
E. None of these

Sol. Lets assume suesh's age to be 4x in 2016
And ramesh's age to be 5x in 2016

In 2006 suresh's age is = 4x/2 = 2x
In 2006 ramesh's age is = 5x*(3/5) = 3x

In 2016, sures's age will be = (2x+10), which is given to be 4x, thus equating the two,

4x = 2x + 10

x = 5

Thus suresh's age in 2026 will be = 4x + 10 = 4*5 + 10 = 30 yrs.

3. In right triangle ABC, the perimeter is given to be 12cm. The ratio of base to height is 4:3. Find the area of the triangle ?

A. 3
B. 4
C. 6
D. 5
E. None of these

Sol. Lets assume the base and height to be 4x and 3x respectively.

Now, hypotenuse = 5x  ( by pythagoras theorem)

Th perimeter is given to be 12cm, so,

4x+3x+5x = 12

x = 1

Thus the area will be,

= (base*height)/2
= 4*3/2

= 6

4. Two trains of equal lengths when travel in opp. direction crosses each other in 36 seconds, but when travel in same direction faster one crosses the slower one in 60 seconds. Find the ratio of the speeds ?

A. 4:1
B. 3:1
C. 2:1
D. 5:1
E. None of these

Sol. Lets assume length of the train to be 'L'.
And speed of faster train to be 'a'
Speed of slower train to be 'b'

When travelling opp., keeping slower one stationary,

L/(a+b) = 36

When traveeling in same direction, keeping slower one stationary,

L/(a-b) = 60

Solving these two equations,
2a = 8b

a/b = 4/1

Thus , a:b = 4:1

5. A merchant sold an article at a profit of 40%. Had he bought the article for 20% less and sold it at a discount of 20%, he would have gained Rs. 224. What was the merchant’s profit from the sale of the article?

A Rs.700
B Rs.280
C Rs.560
D Rs.980
E.None of these 

Sol. Asume the cost price to be = Rs 100x
Now, selling price will be = Rs 140x   (as 40 % profit)

If the article is bought for 20% less, cost price becomes = Rs 80x
After 20% dicount selling price is = 140x - (20*140x/100) = Rs 112x

Now Profit for this is given Rs 224, so,

112x-80x = 224

x=7

Now original cost price = 100*7 = Rs 700
And selling price = 140*7 = Rs 980

Thus profit is = Rs (980-700) = Rs 280.

6. Find sum of all possible products of first 10 natural numbers taken two at a time.

A. 1600
B. 1540
C. 1260
D. 1320
E. None of these

Sol. (Sum of 10 natural nuumbers)^2 = Sum of the squares of first 10 natural numbers + 2*(Required Sum)

Sum of first 10 natural nuumbers = 10*(10+1)/2 = 55
Sum of the squares of first 10 natural numbers = 10(10+1)(10*2 + 1)/6 = 385

Thus,

(55)^2 = 385 + 2(Required Sum)

Required Sum = 1320.

7. Two trains T1 and T2 are entering on either sides of platform P from opposite ends. Trains T1 and T2 take 20 seconds each to cross the platform and 10 seconds to cross each other. Which of the following could represent the lengths of T1, T2 and P respectively?

A. 250, 300, 350
B. 300, 350, 400
C. 225, 375, 300
D. 275, 350, 625
E. None of these

Sol. Lets assume the speeds of the trains to be 'a' and 'b'
Length of the trains to be 'x' and 'y'
Length of the platform to be 'p'

Thus,
(x+p)/a = 20
(y+p)/b = 20
(x+y)/(a+b) = 10

Solving these three, we get,

(x+y)=2p

Thus checking options the answer is C.

8. A man rows upstream 16 km and downstream 27 km talking 5 hours each time. What is the velocity of current?

A. 2 km/hr
B. 2.1 km/hr
C. 1.1 km/hr
D. 1.4 km/h
E. None of these

Sol. Man’s rate upstream=16/5 km/hr
Man’s rate downstream=27/5 km/hr
Velocity of the current=(1/2)*(27/5-16/5) km/hr=1.1 km/hr

9. In Times Model School, 60% of the students are boys. In an aptitude test, 80% of the girls scored more than 40 marks (out of a maximum possible 150 marks). If 60% of the total students scored more than 40 marks in the same test, find the fraction of the boys who scored 40 marks or less?

A. 3/5 
B. 6/7  
C. 5/7
D. 7/15 
E. none of these

Sol. Let the total number of students be y. Then,
Number of boys=3y/5
Number of girls=2y/5
Number of girls scoring more than 40 marks=4/5×2y/5=8y/25
Total number of students scoring more than 40 marks=3y/5
? Required fraction =7/25×5/3=7/15
Hence, the fraction of the boys who scored 40 marks or less is 7/15.

10. A man can row three quarters of a km against the stream in 11 minutes 15 seconds ad return in 7 minutes 30 seconds. Find the speed of the man in still water and also the speed of the stream ?

A. 5 km/hr, 2 km/hr
B. 5 km/hr, 1 km/hr
C. 6 km/hr, 2 km/hr
D. 4 km/hr, 1 km/hr
E. None of these 

Sol. Rate upstream=3/4 * 4/45 * 60=4 km/hr
Rate downstream=3/4 * 2/15 * 60=6 km/hr
Speed of the man in still water (6+4)/2=5 km/hr
Speed of the stream=(6-4) ½=1 km/hr

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