BANK & INSURANCE (PERCENTAGE) PART 2

Total Questions: 60

31. Out of her income of Rs. 24,000, Shefali spent 35% on rent, Rs. 2,000 on food and saved the rest. Later, Shefali’s income increased by 25% and her expense on rent and food increased by Rs. 600 and 15%, respectively. How much does Shefali save now?

Correct Answer: (d) Rs. 18,700 
Solution:

Amount initially spent by Shefali on rent = 24000 × 0.35 = Rs. 8,400
Increased amount spent on Rent = 8400 + 600 = Rs. 9,000
Amount initially spent by Shefali on food = Rs. 2,000
Increased amount spent on food = 2000 × 1.15 = Rs. 2,300 Increased income of Shefali = 24000 × 1.25 = Rs. 30,000
So, new savings of Shefali = 30000 − (9000 + 2300) = Rs. 18,700

32. Ratio of number of boys and girls in a school is 4:3, respectively. Number of boys who like Burger is 50% more than number of girls who like Pizza and ratio between number of girls who like pizza and number of girls who like burger is 1:2, respectively. Find the total number of students in the school, if the difference between number of boys and number of girls, who like Pizza is 135. It is known that each student in the school like either burger or pizza.

Correct Answer: (a) 630 
Solution:

Let the total number of students in the school be 70x
So, number of boys in the school = 70x × (4/7) = 40x
And, number of girls in the school = 70x − 40x = 30x

Number of girls who like Pizza = 30x × (1/3) = 10x
Number of girls who like Burger = 30x − 10x = 20x
Number of boys who like burger
= 10x + 10x × 0.5 = 15x
Number of boys who like Pizza = 40x − 15x = 25x
According to question:
25x − 10x = 135
15x = 135
x = 9
Total number of students in the school
= 70x = (9 × 70) = 630

33. The ratio of incomes of A and B is 8:9, respectively. If A and B spends 25% and (100/3)% of their respective incomes, then find the sum of their incomes given that the difference between their expenditures is Rs. 4,000?

Correct Answer: (c) Rs. 68,000
Solution:Let the incomes of A and B be Rs. 8x and Rs. 9x, respectively. Expenditure of A = 25% of 8x = Rs. 2x
Expenditure of B = (100/3)% of 9x = Rs. 3x
Difference between their expenditure
= 3x − 2x = Rs. x
Given, x = 4000
So, the income of A = 8x = 8 × 4000 = Rs. 32,000
And, the income of B = 9x = 9 × 4000
= Rs. 36,000
The sum of their incomes
= 36000 + 32000 = Rs. 68000

34. Out of total monthly income of Vinod, he spent 25% on paying rent and 20% of the remaining on buying groceries. Out of the amount left after paying rent and buying groceries, he spent 30% of that on paying electricity bill and then distributed the remaining amount between A and B in the ratio of 9:5, respectively. If the amount received by A is Rs. 8,100, then find the monthly income of Vinod.

Correct Answer: (d) Rs. 30,000 
Solution:

Let the monthly salary of Vinod be Rs. 100x
So, amount spent on paying rent = 100x × 0.25 = Rs. 25x Amount spent on buying groceries = (100x − 25x) × 0.2 = Rs. 15x Amount spent on paying electricity bills = (100x − 25x − 15x) × 0.3 = Rs. 18x Remaining amount
= 100x − (25x + 15x + 18x) = Rs. 42x
Amount received by A = 42x × (9/14) = Rs. 27x
According to question:
27x = 8100
So, x = 300
So, monthly income of Vinod = 100x
= 100 × 300 = Rs. 30,000

35. Incomes of A and B are in ratio 4:7, respectively. If A and B save Rs. 3,000 and Rs. 6,000, respectively and expenditure of A is 40% less than that of B. The average income of A and B is how much percent more/less than savings of B?

Correct Answer: (c) 175%
Solution:

Let the income of A and B be Rs. 4x and 7x respectively.
Let the expenditure of B be Rs. y;
So, the expenditure of A = y × 0.6 = Rs. 0.6y;
4x − 0.6y = 3000 … (I)
7x − y = 6000 … (II)
On subtracting 0.6 × equation (II) from equation (I), we have; 0.2x = 600
Or, x = 3000
Therefore, average income of A and B = {(4x + 7x)/2} = Rs. 16500 Required percentage = ((16500 − 6000)/6000) × 100 = 175%

36. Raj and Rohit together have total of Rs. 4,000 out of which they donated 10% to the charity. The remaining amount is to be then redistributed between them in such a manner that Raj gets 40% more amount than Rohit. If the amount received by Raj is Rs. P, then find the value of √[(P/7) + 21].

Correct Answer: (a) 11 
Solution:Let the amount received by Rohit be Rs. x
Therefore, amount received by Raj = 1.40 × x = Rs. 1.4x ATQ:
(x + 1.4x) = 4000 × 0.9
2.4x = 3600
x = 1500
So, share of Raj = 3600 − 1500 = Rs. 2,100
So, 2100 = 3P
P = 700
So, required value = √((700/7) + 21) = √(100 + 21) = 11

37. Incomes of A and B are in the ratio 4:3, respectively. Savings of A and B are in the ratio 3:1, respectively. If they both spend Rs. 5,000, each, then find the difference between their average incomes and average savings.

Correct Answer: (e) Rs. 5,000
Solution:

Let the incomes of A and B be Rs. 4x and Rs. 3x, respectively. ATQ;
((4x − 5000)/(3x − 5000)) = (3/1)
4x − 5000 = 9x − 15000
Or, 10000 = 5x
So, x = 2000
So, average incomes of A and B = ((4x + 3x)/2)
= 3.5x = 3.5 × 2000 = Rs. 7,000 Savings of A
= 4x − 5000 = Rs. 3,000
Savings of B = 3x − 5000 = Rs. 1,000
So, their average savings = ((3000 + 1000)/2)
= Rs. 2,000
Required difference = 7000 − 2000 = Rs. 5,000

38. In 2021, out of his income of Rs. 35,000, Mohan spent 20% on rent, 30% of the remaining income on groceries and saved the rest. In 2022, Mohan spent 15% more on rent, Rs. 550 more on grocery and saved Rs. 400 more, compared to 2021. By how much did his income increase in 2022 as compared to 2021?

Correct Answer: (a) Rs. 2,000 
Solution:Mohan’s rent expense in 2021 = 35000 × 0.2
= Rs. 7,000
Remaining income = 35000 − 7000 = Rs. 28,000
Mohan’s grocery expense in 2021 = 28000 × 0.3
= Rs. 8,400 Mohan’s savings in 2021 = 35000 − (7000 + 8400) = Rs. 19,600 Mohan’s rent expense in 2022 = 7000 × 1.15 = Rs. 8,050
Mohan’s grocery expense in 2022 = 8400 + 550
= Rs. 8,950 Mohan’s savings in 2022 = 19600 + 400 = Rs. 20,000
So, Mohan’s income in 2022 = 8050 + 8950 + 20000
= Rs. 37,000 So, increase in income = 37000 − 35000
= Rs. 2,000

39. A bucket is filled with water such that the weight of bucket alone is 25% its weight when it is filled with water. Now some of the water is removed from the bucket and now the weight of bucket along with remaining water is 50% of the original total weight. What part of the water was removed from the bucket?

Correct Answer: (c) 2/3
Solution:

Let original weight of bucket when it is filled with water = x
Then weight of bucket = (25/100) × x = x/4
Original weight of water = x − (x/4) = 3x/4
Now when some water removed, new weight of bucket with remaining water = (50/100) × x = x/2
So new weight of water = new weight of bucket with remaining water − weight of bucket = (x/2) − (x/4) = x/4
So part of water removed = [(3x/4) − (x/4)]/(3x/4)
= 2/3

40. If the price of wheat is reduced by 2%. How many kilograms of wheat a person can buy with the same money which was earlier sufficient to buy 49 kg of wheat?

Correct Answer: (e) 50 kg
Solution:

Let the original price = 100 Rs per kg
Then money required to buy 49 kg
⇒ 49 × 100 = Rs 4900
New price per kg is (100−98)% of Rs 100 = 98
So quantity of wheat bought in 4900 Rs is
4900/98 = 50 kg