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Given:

The amount that Abhishek got = ₹ 1580

Spending on rent, petrol, and food in terms of ratio = (1/5) : (1/3) : (1/8)

Concept used:

If ratio is in fraction = (1/a) : (1/b) : (1/c)

Then take the L.C.M of a, b & c

New ratio = bc : ac : ab

Calculation:

Take L.C.M of 5, 3, and 8

L.C.M = 120

New ratio of spending = 24 : 40 : 15

Total spending in terms of ratio = 24 + 40 + 15 = 79 units

Equating the total amount,

79 → ₹ 1580

⇒ 15 → (1580/79) × 15 = ₹ 300

∴ The amount spent on food is ₹ 300.

Given speed of slower train V1 = 45 km/h

Let the speed of faster train V2 = V km/h

Since both the trains are moving in parallel direction.

∴ Relative speed = V2 – V1 = V – 45

∴ To cross a man in the smaller train longer train has to cross it’s own length with relative speed

Time taken to cross the 110 m length = 18 s

Speed = Distance/Time

⇒ (V – 45) × (1000/3600) = 110/18               (since 1 km/h = (1000/3600) m/s)

 ⇒ V – 45 = (110/18) × (3600/1000)             [(3600/1000) m/s = 1 km/h]

⇒ V – 45 = 22

⇒ V = 67 km/h

∴ Speed of longer train = 67 km/h

Given:

Husband's age = 4 × son's age 

Wife's age = husband's age - 9

Sum of ages = 99 years

Calculation:

Let husband's age be 4x.

∴ Son's age = x, wife's age = 4x - 9

A.T.Q

4x + x + 4x -9 = 99 years

⇒ 9x = 108

⇒ x = 12 years

Husband's age = 12 × 4 = 48 years

Wife's age = 48 - 9 = 39 years

Required ratio = 48 : 39 : 12 = 16 : 13 : 4

∴ The ratio is 16 : 13 : 4

Given:

Three successive discounts of 20%, 10% and 5% respectively.

Profit = ₹ 52

Concept Used:

Profit = S.P - C.P

Profit% = (Profit/C.P) × 100

Calculation:

Let C.P. of Cycle = ₹ 100x

M.P. of Cycle = ₹ 150x

S.P. of Cycle = 150x × (80/100) × (90/100) × (95/100)

⇒ ₹ 102.6x

According to the question

⇒ 102.6x - 100x = 52

⇒ x = 20

C.P. of Cycle = 100 × 20 = ₹ 2000

For 25% of profit

S.P. of Cycle = 2000 × (125/100)

⇒ ₹ 2500

∴ Price man sold the cycle to make a profit of 25% is ₹ 2500.

Ratio of time taken by A and B to complete a work = 2 ∶ 3

∴ Ratio of efficiency of A and B = 3 ∶ 2

Let, efficiency of A = 3x/day and efficiency of B = 2x/day

Let, quantity of total work = a

According to problem,

⇒ 5 × 3x + 10 × 2x = 0.7a

⇒ 0.7a = 35x

⇒ a = 50x

Let, they together do the work in = y days

⇒ y × (3x + 2x) = 50x

⇒ y = 50x/5x

⇒ y = 10

∴ They together will complete the work in = 10 days

3 men can do a piece of work in 12 days

1 man will do the same piece of work in 36 days

5 women will do the same piece of work in 8 days

1 woman will do the same piece of work in 40 days

20 children can do a piece of work in 3 days

1 child will do the same piece of work in 60 days

Now, (1 man + 1 woman + 1 child)’s 1 day work

$\frac{1}{{36}} + \frac{1}{{40}} + \frac{1}{{60}}=\frac{5}{{72}}$

So, the work is complete in $\frac{{72}}{5} = 14\frac{2}{5}$ days

Simple interest on Rs. 33880 at the rate of 25% for 1 year = (33880 × 25 × 1) /100 = Rs. 8470

Rate of Compound interest = 10%

Assume Rs. x = 1000

The chart for compound interest on Rs. 1000 for 3 years at the rate of 10% per annum will be as

 

                                      Rs. 1000 (Principal)

1^st year                          2^nd year                     3^rd year

Rs. 100                          Rs. 100                      Rs. 100

                                      Rs. 10                        Rs. 10

                                                                        Rs. 10

                                                                        Rs. 1

Compound interest for 3^rd year = Rs. 100 + Rs. 10 + Rs. 10 + Rs. 1 = Rs. 121

But the compound interest is = Rs. 8470 (given)

⇒ 121y = 8470

⇒ y = 70

∴ The amount given on Compound interest = Rs. 1000 × 70 = Rs. 70000

GIVEN:

Investment of A and B is Rs. 64000

A decreased the amount by Rs. 5000 each year and B increased the amount by Rs. 4000 each year

 

FORMULA USED:

Profit = Investment x time

 

ASSUMPTION :

Let the amount invested by A and B in the first year be a and b respectively.

⇒ a + b = Rs. 64000

 

CALCULATION :

According to the question,

A decreased the amount by Rs. 5000 each year and B increased the amount by Rs. 4000 each year

Amount invested by A in the four years = a + a – 5000 + a – 10000 + a – 15000 = 4a – 30000

Amount invested by B in the four years = b + b + 4000 + b + 8000 + b + 12000 = 4b + 24000

Ratio = (4a – 30000) : (4b + 24000) = a – 7500 : b + 6000

The ratio of their profits is 13 : 12

⇒ a – 7500 : b + 6000 = 13 : 12

⇒ a + b = 64000

Putting b = 64000 – a, we get

⇒ (a – 7500) : (64000 – a + 6000) = 13 : 12

⇒ (a – 7500)/(64000 – a + 6000) = 13/12

⇒ 12a – 12(7500) = 13(70000) - 13a

⇒ 25a = 1000000

⇒ a = 40000

∴ Amount invested by A is Rs. 40000

Quantity of first mixture taken = 10 litres

∴ Amount of spirit = 2/5 × 10 = 4 litres

⇒ Amount of water = 6 litres

Let the quantity of second mixture be x litres

∴ Amount of spirit = 3/5 × x = 3x/5 litres

⇒ Amount of water = 2x/5 litres

Now, total quantity of mixture = (10 + x) litres

∴ Amount of spirit = 4/9 × (10 + x) = 4(10 + x)/9 litres

Total spirit = spirit from first container + spirit from second container

∴ 4(10 + x)/9 = 4 + 3x/5

⇒ 20 × (10 + x) = 180 + 27x

⇒ 200 + 20x = 180 + 27x

⇒ 20 = 7x

⇒ x = 2.86 litres

Given:

Total number of students = 30

Average marks of 30 students = 76

Formula used:

Average marks = total marks obtained by all students/number of students

Calculation:

Total marks obtained by 30 students = 76 × 30 = 2280

∵ Two marks were wrongly read, so we shall subtract wrong marks from total marks and then add actual marks in total marks

⇒ 2280 – (78+ 52) + (82 + 60)

⇒ 2280 – 130 + 142 = 2292

Actual correct marks = 2292

Now, the correct average = 2292/30 = 76.4

∴ The correct average is 76.4

Shortcut Trick Difference between the wrongly read and the actual marks 

78 - 82 = - 4

52 - 60 = - 8

Total difference = - 12

Then, change in average marks = 76 + 12/30 = 76.4

For negative value we add in the average.

And for positive value we subtract in the average.