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Question 1 of 5
1. Question
The monthly incomes of Amit and Bharat are in the ratio of 5:4. Their monthly expenses are in the ratio 4:3. If each saves ₹5,000 per month, what are their monthly incomes?
Correct
Answer: (a)
Solution:
Let incomes be:
Amit = 5x, Bharat = 4x
Expenses:
Amit = 4y, Bharat = 3y
Savings = Income − Expense = ₹5000 for bothSo:
5x − 4y = 5000 …(i)
4x − 3y = 5000 …(ii)Multiply (i) by 3:
15x − 12y = 15000
Multiply (ii) by 4:
16x − 12y = 20000
Subtract:
(16x − 15x) = (20000 − 15000)
x = 5000
Then y = (5x − 5000) / 4 = (25000 − 5000)/4 = 5000So incomes:
Amit = 5x = ₹25,000
Bharat = 4x = ₹20,000Hence, option (A) is correct.
Incorrect
Answer: (a)
Solution:
Let incomes be:
Amit = 5x, Bharat = 4x
Expenses:
Amit = 4y, Bharat = 3y
Savings = Income − Expense = ₹5000 for bothSo:
5x − 4y = 5000 …(i)
4x − 3y = 5000 …(ii)Multiply (i) by 3:
15x − 12y = 15000
Multiply (ii) by 4:
16x − 12y = 20000
Subtract:
(16x − 15x) = (20000 − 15000)
x = 5000
Then y = (5x − 5000) / 4 = (25000 − 5000)/4 = 5000So incomes:
Amit = 5x = ₹25,000
Bharat = 4x = ₹20,000Hence, option (A) is correct.
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Question 2 of 5
2. Question
A person buys three articles A, B, and C for ₹3960. If A costs 20% more than C, and C costs 25% more than B, then what is the cost of A?
Correct
Answer: C
Solution:
Let the cost of B be ₹x.
Then, C = 125% of B = (5/4)x
A = 120% of C = (6/5) × (5/4)x = (6/4)x = (3/2)xNow, total cost = A + B + C
= (3/2)x + x + (5/4)x
= (6x + 4x + 5x)/4 = 15x/4Given total cost = ₹3960
⇒ 15x/4 = 3960 ⇒ x = (3960 × 4)/15 = ₹1056Therefore,
Cost of A = (3/2) × 1056 = ₹1584Incorrect
Answer: C
Solution:
Let the cost of B be ₹x.
Then, C = 125% of B = (5/4)x
A = 120% of C = (6/5) × (5/4)x = (6/4)x = (3/2)xNow, total cost = A + B + C
= (3/2)x + x + (5/4)x
= (6x + 4x + 5x)/4 = 15x/4Given total cost = ₹3960
⇒ 15x/4 = 3960 ⇒ x = (3960 × 4)/15 = ₹1056Therefore,
Cost of A = (3/2) × 1056 = ₹1584 -
Question 3 of 5
3. Question
A man borrowed a sum from a bank to be repaid in equal monthly installments without interest. After paying 12 installments, he found that 40% of the total loan was cleared. How many installments were there in the agreement?
Correct
Answer: (d)
Solution:
Let total loan amount = T
Let installment amount = AAfter 12 installments:
12 × A = 40% of T = (40/100) × T
⇒ 12A = 0.4T
⇒ T/A = 12 / 0.4 = 30Total number of installments = T / A = 30
Incorrect
Answer: (d)
Solution:
Let total loan amount = T
Let installment amount = AAfter 12 installments:
12 × A = 40% of T = (40/100) × T
⇒ 12A = 0.4T
⇒ T/A = 12 / 0.4 = 30Total number of installments = T / A = 30
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Question 4 of 5
4. Question
A person took a loan of ₹20,000 at 10% compound interest per annum. He paid ₹7,000 at the end of the first year and ₹7,700 at the end of the second year. How much should he pay at the end of the third year to clear all dues?
Correct
Answer: (b)
Solution:
Principal = ₹20,000
Interest rate = 10% compounded yearlyAfter 1st year:
Interest = 10% of 20,000 = ₹2,000
Total = 20,000 + 2,000 = ₹22,000
Paid = ₹7,000
Remaining = ₹15,000After 2nd year:
Interest = 10% of 15,000 = ₹1,500
Total = 15,000 + 1,500 = ₹16,500
Paid = ₹7,700
Remaining = ₹8,800After 3rd year:
Interest = 10% of 8,800 = ₹880
Total = 8,800 + 880 = ₹9,680Incorrect
Answer: (b)
Solution:
Principal = ₹20,000
Interest rate = 10% compounded yearlyAfter 1st year:
Interest = 10% of 20,000 = ₹2,000
Total = 20,000 + 2,000 = ₹22,000
Paid = ₹7,000
Remaining = ₹15,000After 2nd year:
Interest = 10% of 15,000 = ₹1,500
Total = 15,000 + 1,500 = ₹16,500
Paid = ₹7,700
Remaining = ₹8,800After 3rd year:
Interest = 10% of 8,800 = ₹880
Total = 8,800 + 880 = ₹9,680 -
Question 5 of 5
5. Question
A principal amount becomes in one year when compounded quarterly at an annual interest rate of . If the same amount becomes in one year when compounded annually at , which one of the following is correct?
Correct
Answer: C
Solution:
Let’s assume , and test with a 12% annual rate:If compounded quarterly:
Each quarter rate = 12% / 4 = 3%
Amount after 1 year =If compounded annually at 12%:
Amount =Thus, for the same amount , the quarterly compounding gives more than annual.
So to reach the same , S > RIncorrect
Answer: C
Solution:
Let’s assume , and test with a 12% annual rate:If compounded quarterly:
Each quarter rate = 12% / 4 = 3%
Amount after 1 year =If compounded annually at 12%:
Amount =Thus, for the same amount , the quarterly compounding gives more than annual.
So to reach the same , S > R
