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Let the two numbers be x and y.

Given,

xy = 2500

And x is four times y.

⇒ x = 4y      ----(1)

Putting the value of x in (1), we get

⇒ 4y² = 2500

⇒ y² = 625

⇒ y = 25

The numbers are x = 4 × y = 100 and y = 25

Sum of two numbers = 100 + 25 = 125

Shortcut Trick

Speed ratio P : Q is 11 : 16. Difference = 5 units = 25 km/h ⇒ 1 unit = 5 km/h.

Speed of P = 11 × 5 = 55 km/h; Speed of Q = 16 × 5 = 80 km/h.

Relative speed = 55 + 80 = 135 km/h. Meeting time = 1 hr 36 min = 8/5 hr.

Total Distance XY = 135 × (8/5) = 27 × 8 = 216 km.

Time for P = Distance ÷ Speed of P = 216 / 55 hr.

∴ The correct answer is 216/55 hr.

Alternate Method

Given: Speed ratio P:Q = 11:16, Speed difference = 25 km/h, Meeting time = 1 hr 36 min.

Formula Used: Speed = Distance ÷ Time; Relative Speed (Opposite) = S₁ + S₂.

⇒ Let speeds be 11k and 16k. Difference = 16k − 11k = 5k.

⇒ 5k = 25 ⇒ k = 5 km/h.

⇒ Speed of P = 55 km/h, Speed of Q = 80 km/h.

⇒ Meeting time = 1 + 36/60 = 1 + 3/5 = 8/5 hours.

⇒ Total Distance = Relative Speed × Meeting Time = (55 + 80) × (8/5) = 135 × (8/5) = 216 km.

⇒ Time taken by P = Total Distance ÷ Speed of P = 216 / 55 hr.

∴ The correct answer is 216/55 hr.

Additional Information

Relative Speed

When two objects move in opposite directions, their relative speed is the sum of their individual speeds (S₁ + S₂).

Meeting Time Logic

Total Distance = Relative Speed × Time taken to meet, provided they start moving at the same time.

Time and Speed Relation

For a constant distance, the time taken is inversely proportional to the speed (T ∝ 1/S).

Given:

The perimeters of two squares plots are 52 cm and 20cm

Concept used:

The perimeter of square = 4 × side

The area of a square = (side)2

Calculation:

Side of the first square = 52 ÷ 4 = 13 cm and

Side of the second square = 20 ÷ 4 = 5 cm

Now, the difference in their areas = 13² – 5² = 144 cm²

Then, sides of the new square = √144 = 12 cm

Now, perimeter of new square = 4 × 12 = 48 cm

∴ The perimeter of the third square is 48 cm

Given:

The difference between simple interest and compound interest (compounding of interest is done annually) on a certain sum of money for 3 years at the rate of 20 percent per annum is Rs. 192. 

Formula used:

Difference between CI and SI in 3 yr = P( R /100)² {( R/100) + 3}

Calculation:

Let the principal is P

As per the question,

⇒ 192 = P( 20 /100)2 {( 20/100) + 3}

⇒ 192 = P( 1/5)2 {( 1/5 + 3}

⇒ P = 4800 / 3.2

⇒ P = Rs 1500

∴ The correct option is 3

Given:

Mansi and Taruna have money in the ratio 5: 7

Taruna and Renu have it in the ratio 8 : 11

Taruna has Rs. 2240

Calculation:

Mansi: Taruna = 5: 7 ....(× 8)

Taruna: Renu = 8: 11 ....(× 7)

Mansi: Taruna: Renu = 40: 56: 77

56 → 2240

1 → 2240/56 = 40

77 → 77 × 40 = 3080

The answer is 3080.

Given:

The average age of 4 members 5 years ago = 22 years

The average age of the family is the same as what it was 5 years ago after the baby is born.

Formula used:

The sum of ages = Average × Number of family members

Calculation:

Total age of 4 members of the family at present = 27 × 4 years

⇒ 108 years

The present age of 5 members would have been = 22 × 5 = 110

Age of baby = (110 - 108) years

⇒ 2 year

∴ The age of baby is 2 year

Given:

Rs. 3550 is divided into X, Y and Z

three times of X's share is equal to 5 times of Y's share and 7 times of Z's share.

Solution:

3X = 5Y

⇒ Y = $\dfrac{3X}{5}$

3X = 7Z

⇒ Z = $\dfrac{3X}{7}$

X + Y + Z = 3550

⇒ X + $\dfrac{3X}{5}$ + $\dfrac{3X}{7}$ = 3550

⇒ 35X + 21X + 15X = 124250

⇒ X = $\dfrac{124250}{71}$ = 1750

Share of X = Rs. 1750

GIVEN:

Sum of their monthly salary = Rs60000

A's expenditure = 80% of his salary 

B's expenditure = 90% of his salary

A's savings = B's savings

EXPLANATION:

Let A's salary be x

∴ B's salary = 60000 - x

A's savings = 20% of x = $\frac{x}{5}$

B's savings = 10% of (60000 - x) = $\frac{60000 - x}{10}$

$\therefore \frac{x}{5} = \frac{60000 - x}{10}$ ⇒ $x = 20000$

B's salary = $60000 - 20000 = 40000$

Alternate Method

$20\% \ of \ A = 10\% \ of \ B$

$\Rightarrow \frac{A}{B} = \frac{1}{2}$

$\Rightarrow A + B = 3 \space ratio$

$3\space ratio = 60000 \Rightarrow 1\space ratio = 20000$

$B's\space salary = 2\space ratio = 40000$

Given:

Ravi spends 70% of his income. His income increases by 25% and his expenditure also increases by 10%

Concept used:

Income - Expenses = Saving

Calculation:

Let the income be 100p

According to the question:

Ravi spends 70% of his income

Expenses = 70p

⇒ 100p - 70p = 30p

Savings = 30p

Income increases by 25% 

⇒ 100p + 25p = 125p

Expenditure increases by 10% 

⇒ 70p + 70p × 10/100 = 77p 

Savings = 125p - 77p = 48

Saving Increase% = (48 - 30)/30 × 100

= 60%

The answer is 60%

Calculation:

Total number of donuts sold by stores P and R together in October = 125 + 960

⇒ 1085

Total number of donuts sold by stores R and Q together in October = 905 + 960

⇒ 1865

Ratio = 1085 : 1865

⇒ 217 : 373

∴ The required answer is 217 : 373.