Explanation

Let marker = M and pen = P.

Equation 1:
3M + P = 245

Equation 2:
3M + 3P = 345

Subtract Equation 1 from Equation 2:

3P − P = 345 − 245
2P = 100
P = 50

Now:

3M + 50 = 245
3M = 195
M = 65

Explanation

Given:

• Train length = 90 m
• Tunnel length = 231 m
• Time = 11 seconds

Distance covered = 90 + 231 = 321 m

Speed = Distance ÷ Time
= 321 ÷ 11 = 29.18 m/s

Convert to km/h:

29.18 × 18/5 = 105.05 km/h

Explanation

1. Current Ages:

   • Let Zoya’s current age be $x$
   • Then, Zaid’s current age is $6x$ (since he is six times as old as Zoya).

2. The sum of Ages in 7 Years:

   • In 7 years, Zoya's age will be $x + 7$ and Zaid's age will be $6x + 7$.
   • The sum of their ages in 7 years will be $(x+7)+(6x+7)=49$.

Step 1: Formulate the Equation

x+7+6x+7=49
$$7x+14=49$$

Step 2: Solve for $x$

Subtract 14 from both sides:

$$7x=35$$

Now divide by 7:

$$x=5$$

So, Zoya’s current age is $5$ years and Zaid’s current age is:

$$6x=6\times 5=30$$

Step 3: Determine Zaid’s Age When Zoya Was Born

When Zoya was born, Zaid would have been:

$$30-5=25$$

Explanation

Given:

a : b : c = 3 : 4 : 7

We need to find (a + b + c) : c

Step 1: Add the ratios:

3 + 4 + 7 = 14

Step 2: The value of c = 7

Step 3: Form the ratio:

14: 7

Step 4: Simplify:

14 : 7 = 2 : 1

Explanation

5 → 25, so multiplier = 25 ÷ 5 = 5

Second quantity = 8 × 5 = 40