The homework problems are: 27. 6.68 × 6.4 = ?, 28. If A:B=2:3; B:C=4:5 then A:B:C = ?, 29. If total salary of…

Question

The homework problems are: 27. 6.68 × 6.4 = ?, 28. If A:B=2:3; B:C=4:5 then A:B:C = ?, 29. If total salary of A and B is Rs.45000 and their ratio of salary is 7:3, then find the salary of A.

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the problems:

27. $6.68 \times 6.4$

Multiply the numbers.
$6.68 \times 6.4 = 42.752$
The correct option is (c).
$\boxed{\text{42.752}}$
28. If A:B=2:3; B:C=4:5 then A:B:C=?
Write the given ratios.
$A:B = 2:3$ $B:C = 4:5$
Make the value of B common in both ratios.
The least common multiple of 3 and 4 is 12.
Multiply the first ratio by 4:
$A:B = (2 \times 4) : (3 \times 4) = 8:12$
Multiply the second ratio by 3:
$B:C = (4 \times 3) : (5 \times 3) = 12:15$
Combine the ratios.
$A:B:C = 8:12:15$
The correct option is (c).
$\boxed{\text{8:12:15}}$
29. If total salary of A and B is Rs.45000 and their ratio of salary is 7:3, then find the salary of A.
Let the salaries of A and B be $7x$ and $3x$ respectively.
The total salary is Rs.
$7x + 3x = 45000$ $10x = 45000$ $x = \frac{45000}{10}$ $x = 4500$
Find the salary of A.
$\text{Salary of A} = 7x = 7 \times 4500 = 31500$
The correct option is (a).
$\boxed{\text{Rs. 31500}}$
30. $9999 + 3333 - 6666 = ?$
Perform the addition.
$9999 + 3333 = 13332$
Perform the subtraction.
$13332 - 6666 = 6666$
The correct option is (c).
$\boxed{\text{6666}}$
31. $5978 + 6134 + 7014 = ?$
Add the numbers.
$5978 + 6134 + 7014 = 19126$
The correct option is (b).
$\boxed{\text{19126}}$
32. Find the average of $25+35+45+55+65+75+85+95$ .
Sum the numbers.
$25+35+45+55+65+75+85+95 = 460$
Count the number of values.
There are 8 values.
Calculate the average.
$\text{Average} = \frac{\text{Sum of values}}{\text{Number of values}}$ $\text{Average} = \frac{460}{8}$ $\text{Average} = 57.5$
The given options are (a) 70, (b) 60, (c) 80, (d) 100. None of the options match the calculated average. However, the option (b) 60 is marked as correct in the image. If we assume there might be a typo in the question or options, and the closest integer is desired, 60 is not the closest. Let's recheck the sum.
$25+35=60$
$45+55=100$
$65+75=140$
$85+95=180$
$60+100+140+180 = 480$ .
Let's re-sum carefully:
$25+35+45+55+65+75+85+95 = 480$ .
Calculate the average with the corrected sum.
$\text{Average} = \frac{480}{8}$ $\text{Average} = 60$
The correct option is (b).
$\boxed{\text{60}}$
33. Mr. X bought a car for Rs.1 lakh and sold it at 25% loss. What is the selling price of the car?
Identify the cost price (CP).
$\text{CP} = \text{Rs. } 1 \text{ lakh} = \text{Rs. } 100,000$
Calculate the loss amount.
$\text{Loss} = 25\% \text{ of CP} = 0.25 \times 100,000 = \text{Rs. } 25,000$
Calculate the selling price (SP).
$\text{SP} = \text{CP} - \text{Loss}$ $\text{SP} = 100,000 - 25,000 = \text{Rs. } 75,000$
The correct option is (c).
$\boxed{\text{Rs. 75,000}}$
34. The distance between TPJ and MS is 450 km. The distance is covered by a train in 5 hours. What is the distance covered in 1 hour.
Calculate the speed of the train.
$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$ $\text{Speed} = \frac{450 \text{ km}}{5 \text{ hours}}$ $\text{Speed} = 90 \text{ km/hour}$
The distance covered in 1 hour is equal to the speed.
$\text{Distance in 1 hour} = 90 \text{ km}$
The correct option is (b).
$\boxed{\text{90 km}}$
35. $625 \text{ divided by } 25 + 225 \text{ divided by } 15 + 900 \text{ divided by } 30 = ?$
Perform the divisions according to the order of operations.
$625 \div 25 = 25$ $225 \div 15 = 15$ $900 \div 30 = 30$
Perform the additions.
$25 + 15 + 30 = 70$
The correct option is (d).
$\boxed{\text{70}}$
36. $3, 6, 9, 15, 24, 39, 63, \_$ .
Analyze the pattern.
This is a Fibonacci-like sequence where each term is the sum of the two preceding terms.
$3+6=9$ $6+9=15$ $9+15=24$ $15+24=39$ $24+39=63$
Find the next term.
$39+63=102$
The correct option is (a).
$\boxed{\text{102}}$
37. What is 50% of 75% of 75?
Convert percentages to decimals.
$50\% = 0.50$ $75\% = 0.75$
Calculate 75% of 75.
$0.75 \times 75 = 56.25$
Calculate 50% of the result from Step 2.
$0.50 \times 56.25 = 28.125$
The correct option is (b).
$\boxed{\text{28.125}}$
38. Mr.X 's monthly salary is 28500/- His monthly expenses is 24,000/-. He deposits Rs.3500 per month in a savings account. What is the left over money in his hand at the end of one year?
Calculate total monthly deductions.
$\text{Total monthly deductions} = \text{Monthly expenses} + \text{Monthly savings deposit}$ $\text{Total monthly deductions} = 24000 + 3500 = \text{Rs. } 27500$
Calculate monthly money left in hand.
$\text{Monthly money left} = \text{Monthly salary} - \text{Total monthly deductions}$ $\text{Monthly money left} = 28500 - 27500 = \text{Rs. } 1000$
Calculate money left in hand at the end of one year (12 months).
$\text{Annual money left} = \text{Monthly money left} \times 12$ $\text{Annual money left} = 1000 \times 12 = \text{Rs. } 12000$
The correct option is (b).
$\boxed{\text{Rs. 12000}}$
39. ACE, FHJ, KMO, PRT, Find next three letters?
Analyze the pattern of the first letters of each group.
A (1st letter) $\xrightarrow{+5}$ F (6th letter) $\xrightarrow{+5}$ K (11th letter) $\xrightarrow{+5}$ P (16th letter) $\xrightarrow{+5}$ U (21st letter)
Analyze the pattern of the second letters of each group.
C (3rd letter) $\xrightarrow{+5}$ H (8th letter) $\xrightarrow{+5}$ M (13th letter) $\xrightarrow{+5}$ R (18th letter) $\xrightarrow{+5}$ W (23rd letter)
Analyze the pattern of the third letters of each group.
E (5th letter) $\xrightarrow{+5}$ J (10th letter) $\xrightarrow{+5}$ O (15th letter) $\xrightarrow{+5}$ T (20th letter) $\xrightarrow{+5}$ Y (25th letter)
Combine the next letters.
The next three letters are UWY.
The correct option is (c).
$\boxed{\text{UWY}}$

The homework problems are: 27. 6.68 x 6.4 = ?, 28. If A:B=2:3; B:C=4:5 then A:B:C = ?, 29. If total salary of A and B is Rs.45000 and their ratio of salary is 7:3, then find the salary of A.

Answer

Step-by-step solution

Multiply the numbers.

Write the given ratios.

Make the value of B common in both ratios.

Combine the ratios.

Let the salaries of A and B be $7x$ and $3x$ respectively.

The total salary is Rs.

Find the salary of A.

Perform the addition.

Perform the subtraction.

Add the numbers.

Sum the numbers.

Count the number of values.

Calculate the average.

Calculate the average with the corrected sum.

Identify the cost price (CP).

Calculate the loss amount.

Calculate the selling price (SP).

Calculate the speed of the train.

The distance covered in 1 hour is equal to the speed.

Perform the divisions according to the order of operations.

Perform the additions.

Analyze the pattern.

Find the next term.

Convert percentages to decimals.

Calculate 75% of 75.

Calculate 50% of the result from Step 2.

Calculate total monthly deductions.

Calculate monthly money left in hand.

Calculate money left in hand at the end of one year (12 months).

Analyze the pattern of the first letters of each group.

Analyze the pattern of the second letters of each group.

Analyze the pattern of the third letters of each group.

Combine the next letters.

Try one yourself

Still stuck on this one?

More Mathematics Questions