Topic - Arithmetic

Answer key available? - Yes

Source - Curated Content ]]>

Topic - Arithmetic

Answer key available? - Yes

Source - Curated Content ]]>

Lcm of (6,9) = 18 units

A = 18/6 = 3 units in one day

B = 18/9 = 2 units in one day

So when they work together alternatively

In two days = 3+2 = 5 units

In other two day = 3+2 = 5 units

Again in two day = 3+2 = 5 units

Total

In 6 days = 15 units

Remaining = 18 - 15 = 3 units

Now A turn will come to finish this 3 units of work and he will do it in one day only

So total days they took to complete the work = 6+1 = 7 days

[Solved by Rajendra Rajput]

]]>Water =850ml

Juice = 150ml

Now we are adding water that means juice is still untouched and it's given that now juice is 1 % of the quantity

Clearly

Total = 15000ml

Juice = 150 ml

So water = 14850ml

Water added = 14850-850 = 14000ml I.e 14ltr

[solved by rajendra rajput] ]]>

Remaining 3/4 is done by B in 10 days

So B take 10*4/3 = 40/3 days

Together

1/20 + 3/40

= 5/40

= 1/8

= 8 days

[solved by rajendra rajput]

Condition 1:-

When shyam gets head start of 200m and beaten by 30 sec

2000/R - 1800/S = 30 ---> eq (1)

Condition 2:-

When shyam gets a head start of 3 min and won by 1000m

1000/R - 2000/S = 180 ---> eq (2)

Solving this we will get

R = 25/3 m/s

S = 20/3 m/s

R = 2000 * 3 * /25 = 4 min

S = 2000 * 3/20 = 5 min

Thus time taken by Ram & Shyam to complete the race is 4 min & 5 min

[solved by rajendra rajput]

]]>1/6 - 1/x = 1/10

1/x = 1/6 - 1/10

1/x = 4/60

1/x = 1/15

X = 15 hrs

[solved by rajendra rajput]

]]>1/A + 1/B = 1/C

1/A + 1/(A-5) = 1/(A-9)

Solve this quadratic

You will get

A = 15 Days

[solved by rajendra rajput]

]]>1 * 1/3 + 4 * 2/7 = 1/3 + 8/7 = 31/21

Quantity of milk in the resultant mixture

1 * 2/3 + 4 * 5/7 = 2/3 + 20/7 = 74/21

Required ratio

31/21 : 74/21

= 31 : 74

[solved by rajendra rajput]

]]>So 100m (2x of pool)

Since they meet 17 times

So ram covers 17 * 100 = 1700 m

But race is of 1000m

When ram covers the race I.e 1000m

So shyam covers 1700-1000 = 700m

Ram ---- shyam

1000----> 700

5 ------> ?

5 * 700/1000

= 3.5 m/s

[solved by rajendra rajput]

]]>So A+B = 48/12 = 4 units per day

B+C = 48/16 = 3 units per day

Now,

5A+7B+13C = 48 units

5 (A+B)+2 (B+C)+11C = 48

5 (4)+2 (3)+11C = 48

20+6+11C = 48

11C = 22

C = 2 units

So C does 2 units of work daily

So total time required to complete work alone is 48/2 = 24 days

[solved by rajendra rajput]

]]>360/48 = 7.5

360/60 = 6

360/72 = 5 days.

They'll meet at the time equal to the LCM of (7.5,6,2)

which is 30 days.

[solved by rajendra rajput]

]]>For what duration do they run?

a) 5 minutes

b) 10 minutes

c) 15 minutes

d) 20 minutes

What is the distance covered by Rakesh during the entire session?

a) 4 km

b) 5 km

c) 6 km

d) 8 km

When they run in the opposite direction:

Relative speed = 12 m/s.

So they meet every 600/12 = 50 seconds.

When they meet for the first time, harsh would have run 350m and Rakesh 250m.

LCM of 350 and 600 = 4200

LCM of 250 and 600 = 3000

So they’ll meet at the starting point after covering a total distance of 7200m

Time taken = 4200/7 = 600 sec.

When they run in the same direction:

Relative speed = 2 m/s.

So they meet every 600/2 = 300 seconds.

When they meet for the first time, harsh would have run 2100m and Rakesh 1500m.

LCM of 2100 and 600 = 4200

LCM of 1500 and 600 = 3000

So they’ll meet at the starting point for the second time after covering a total distance of 7200m.

Time taken = 4200/7 = 600 sec.

Total duration = 1200 sec = 20 min.

Since both of them ran for 20 minutes, distance covered by Rakesh

= 5x20x60 = 6000m = 6km

[solved by ADURO team]

]]>a) 400 m

b) 500 m

c) 600 m

d) 700 m ]]>

Let the original speeds of the bullets be 8x and 15x respectively.

Distance covered by them in 3 seconds is 24x and 45x.

Since they are shot in perpendicular direction,

51x = 510

x = 10

Hence their speeds before collision were 80m/s and 150m/s.

After collision, their speeds are 80m/s and 60m/s.

Distance travelled by them in 5 seconds after collision = 400m and 300m respectively.

Since they are perpendicular after collision, distance between them after 5 seconds

[solved by ADURO team]

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